Properties

Label 4235.1228
Modulus $4235$
Conductor $4235$
Order $660$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4235, base_ring=CyclotomicField(660))
 
M = H._module
 
chi = DirichletCharacter(H, M([495,110,402]))
 
pari: [g,chi] = znchar(Mod(1228,4235))
 

Basic properties

Modulus: \(4235\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(660\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4235.dr

\(\chi_{4235}(17,\cdot)\) \(\chi_{4235}(52,\cdot)\) \(\chi_{4235}(68,\cdot)\) \(\chi_{4235}(73,\cdot)\) \(\chi_{4235}(117,\cdot)\) \(\chi_{4235}(138,\cdot)\) \(\chi_{4235}(173,\cdot)\) \(\chi_{4235}(178,\cdot)\) \(\chi_{4235}(222,\cdot)\) \(\chi_{4235}(227,\cdot)\) \(\chi_{4235}(248,\cdot)\) \(\chi_{4235}(283,\cdot)\) \(\chi_{4235}(292,\cdot)\) \(\chi_{4235}(327,\cdot)\) \(\chi_{4235}(332,\cdot)\) \(\chi_{4235}(348,\cdot)\) \(\chi_{4235}(402,\cdot)\) \(\chi_{4235}(437,\cdot)\) \(\chi_{4235}(453,\cdot)\) \(\chi_{4235}(458,\cdot)\) \(\chi_{4235}(502,\cdot)\) \(\chi_{4235}(523,\cdot)\) \(\chi_{4235}(558,\cdot)\) \(\chi_{4235}(563,\cdot)\) \(\chi_{4235}(607,\cdot)\) \(\chi_{4235}(612,\cdot)\) \(\chi_{4235}(633,\cdot)\) \(\chi_{4235}(668,\cdot)\) \(\chi_{4235}(677,\cdot)\) \(\chi_{4235}(712,\cdot)\) ...

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: $\Q(\zeta_{660})$
Fixed field: Number field defined by a degree 660 polynomial (not computed)

Values on generators

\((2542,1816,2906)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{67}{110}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(12\)\(13\)\(16\)\(17\)
\( \chi_{ 4235 }(1228, a) \) \(-1\)\(1\)\(e\left(\frac{457}{660}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{127}{330}\right)\)\(e\left(\frac{39}{55}\right)\)\(e\left(\frac{17}{220}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{53}{132}\right)\)\(e\left(\frac{59}{220}\right)\)\(e\left(\frac{127}{165}\right)\)\(e\left(\frac{503}{660}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4235 }(1228,a) \;\) at \(\;a = \) e.g. 2