Properties

Label 4024.191
Modulus $4024$
Conductor $2012$
Order $502$
Real no
Primitive no
Minimal no
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([251,0,133]))
 
pari: [g,chi] = znchar(Mod(191,4024))
 

Basic properties

Modulus: \(4024\)
Conductor: \(2012\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(502\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2012}(191,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4024.p

\(\chi_{4024}(15,\cdot)\) \(\chi_{4024}(31,\cdot)\) \(\chi_{4024}(55,\cdot)\) \(\chi_{4024}(71,\cdot)\) \(\chi_{4024}(87,\cdot)\) \(\chi_{4024}(103,\cdot)\) \(\chi_{4024}(111,\cdot)\) \(\chi_{4024}(119,\cdot)\) \(\chi_{4024}(127,\cdot)\) \(\chi_{4024}(135,\cdot)\) \(\chi_{4024}(151,\cdot)\) \(\chi_{4024}(159,\cdot)\) \(\chi_{4024}(167,\cdot)\) \(\chi_{4024}(191,\cdot)\) \(\chi_{4024}(215,\cdot)\) \(\chi_{4024}(239,\cdot)\) \(\chi_{4024}(247,\cdot)\) \(\chi_{4024}(279,\cdot)\) \(\chi_{4024}(287,\cdot)\) \(\chi_{4024}(295,\cdot)\) \(\chi_{4024}(303,\cdot)\) \(\chi_{4024}(311,\cdot)\) \(\chi_{4024}(319,\cdot)\) \(\chi_{4024}(327,\cdot)\) \(\chi_{4024}(335,\cdot)\) \(\chi_{4024}(359,\cdot)\) \(\chi_{4024}(375,\cdot)\) \(\chi_{4024}(391,\cdot)\) \(\chi_{4024}(399,\cdot)\) \(\chi_{4024}(407,\cdot)\) ...

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

\((1007,2013,2017)\) → \((-1,1,e\left(\frac{133}{502}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 4024 }(191, a) \) \(1\)\(1\)\(e\left(\frac{417}{502}\right)\)\(e\left(\frac{133}{502}\right)\)\(e\left(\frac{143}{502}\right)\)\(e\left(\frac{166}{251}\right)\)\(e\left(\frac{315}{502}\right)\)\(e\left(\frac{214}{251}\right)\)\(e\left(\frac{24}{251}\right)\)\(e\left(\frac{337}{502}\right)\)\(e\left(\frac{73}{251}\right)\)\(e\left(\frac{29}{251}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4024 }(191,a) \;\) at \(\;a = \) e.g. 2