Properties

Label 4235.1208
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([495,440,336]))
 
pari: [g,chi] = znchar(Mod(1208,4235))
 

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.dq

\(\chi_{4235}(37,\cdot)\) \(\chi_{4235}(53,\cdot)\) \(\chi_{4235}(58,\cdot)\) \(\chi_{4235}(93,\cdot)\) \(\chi_{4235}(102,\cdot)\) \(\chi_{4235}(137,\cdot)\) \(\chi_{4235}(158,\cdot)\) \(\chi_{4235}(163,\cdot)\) \(\chi_{4235}(207,\cdot)\) \(\chi_{4235}(212,\cdot)\) \(\chi_{4235}(247,\cdot)\) \(\chi_{4235}(268,\cdot)\) \(\chi_{4235}(312,\cdot)\) \(\chi_{4235}(317,\cdot)\) \(\chi_{4235}(333,\cdot)\) \(\chi_{4235}(368,\cdot)\) \(\chi_{4235}(422,\cdot)\) \(\chi_{4235}(438,\cdot)\) \(\chi_{4235}(443,\cdot)\) \(\chi_{4235}(478,\cdot)\) \(\chi_{4235}(522,\cdot)\) \(\chi_{4235}(543,\cdot)\) \(\chi_{4235}(548,\cdot)\) \(\chi_{4235}(592,\cdot)\) \(\chi_{4235}(597,\cdot)\) \(\chi_{4235}(653,\cdot)\) \(\chi_{4235}(697,\cdot)\) \(\chi_{4235}(702,\cdot)\) \(\chi_{4235}(718,\cdot)\) \(\chi_{4235}(823,\cdot)\) ...

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

\((2542,1816,2906)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{28}{55}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(12\)\(13\)\(16\)\(17\)
\( \chi_{ 4235 }(1208, a) \) \(-1\)\(1\)\(e\left(\frac{391}{660}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{61}{330}\right)\)\(e\left(\frac{17}{55}\right)\)\(e\left(\frac{171}{220}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{119}{132}\right)\)\(e\left(\frac{147}{220}\right)\)\(e\left(\frac{61}{165}\right)\)\(e\left(\frac{239}{660}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4235 }(1208,a) \;\) at \(\;a = \) e.g. 2