Properties

Label 3021.5
Modulus $3021$
Conductor $3021$
Order $468$
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(3021, base_ring=CyclotomicField(468))
 
M = H._module
 
chi = DirichletCharacter(H, M([234,416,423]))
 
pari: [g,chi] = znchar(Mod(5,3021))
 

Basic properties

Modulus: \(3021\)
Conductor: \(3021\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(468\)
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 3021.ct

\(\chi_{3021}(5,\cdot)\) \(\chi_{3021}(35,\cdot)\) \(\chi_{3021}(74,\cdot)\) \(\chi_{3021}(80,\cdot)\) \(\chi_{3021}(92,\cdot)\) \(\chi_{3021}(101,\cdot)\) \(\chi_{3021}(104,\cdot)\) \(\chi_{3021}(137,\cdot)\) \(\chi_{3021}(161,\cdot)\) \(\chi_{3021}(194,\cdot)\) \(\chi_{3021}(215,\cdot)\) \(\chi_{3021}(233,\cdot)\) \(\chi_{3021}(245,\cdot)\) \(\chi_{3021}(251,\cdot)\) \(\chi_{3021}(263,\cdot)\) \(\chi_{3021}(320,\cdot)\) \(\chi_{3021}(332,\cdot)\) \(\chi_{3021}(359,\cdot)\) \(\chi_{3021}(389,\cdot)\) \(\chi_{3021}(404,\cdot)\) \(\chi_{3021}(416,\cdot)\) \(\chi_{3021}(422,\cdot)\) \(\chi_{3021}(443,\cdot)\) \(\chi_{3021}(446,\cdot)\) \(\chi_{3021}(479,\cdot)\) \(\chi_{3021}(491,\cdot)\) \(\chi_{3021}(503,\cdot)\) \(\chi_{3021}(518,\cdot)\) \(\chi_{3021}(548,\cdot)\) \(\chi_{3021}(557,\cdot)\) ...

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: $\Q(\zeta_{468})$
Fixed field: Number field defined by a degree 468 polynomial (not computed)

Values on generators

\((2015,1750,2281)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{47}{52}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\( \chi_{ 3021 }(5, a) \) \(1\)\(1\)\(e\left(\frac{137}{468}\right)\)\(e\left(\frac{137}{234}\right)\)\(e\left(\frac{95}{468}\right)\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{137}{156}\right)\)\(e\left(\frac{58}{117}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{16}{117}\right)\)\(e\left(\frac{131}{468}\right)\)\(e\left(\frac{20}{117}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3021 }(5,a) \;\) at \(\;a = \) e.g. 2