Properties

Label 6027.872
Modulus $6027$
Conductor $6027$
Order $840$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(840))
 
M = H._module
 
chi = DirichletCharacter(H, M([420,680,63]))
 
pari: [g,chi] = znchar(Mod(872,6027))
 

Basic properties

Modulus: \(6027\)
Conductor: \(6027\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(840\)
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 6027.eu

\(\chi_{6027}(11,\cdot)\) \(\chi_{6027}(53,\cdot)\) \(\chi_{6027}(65,\cdot)\) \(\chi_{6027}(95,\cdot)\) \(\chi_{6027}(149,\cdot)\) \(\chi_{6027}(158,\cdot)\) \(\chi_{6027}(170,\cdot)\) \(\chi_{6027}(179,\cdot)\) \(\chi_{6027}(212,\cdot)\) \(\chi_{6027}(233,\cdot)\) \(\chi_{6027}(317,\cdot)\) \(\chi_{6027}(347,\cdot)\) \(\chi_{6027}(380,\cdot)\) \(\chi_{6027}(464,\cdot)\) \(\chi_{6027}(473,\cdot)\) \(\chi_{6027}(485,\cdot)\) \(\chi_{6027}(527,\cdot)\) \(\chi_{6027}(548,\cdot)\) \(\chi_{6027}(632,\cdot)\) \(\chi_{6027}(641,\cdot)\) \(\chi_{6027}(662,\cdot)\) \(\chi_{6027}(725,\cdot)\) \(\chi_{6027}(767,\cdot)\) \(\chi_{6027}(809,\cdot)\) \(\chi_{6027}(842,\cdot)\) \(\chi_{6027}(872,\cdot)\) \(\chi_{6027}(914,\cdot)\) \(\chi_{6027}(926,\cdot)\) \(\chi_{6027}(956,\cdot)\) \(\chi_{6027}(977,\cdot)\) ...

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: $\Q(\zeta_{840})$
Fixed field: Number field defined by a degree 840 polynomial (not computed)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{17}{21}\right),e\left(\frac{3}{40}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 6027 }(872, a) \) \(1\)\(1\)\(e\left(\frac{209}{420}\right)\)\(e\left(\frac{209}{210}\right)\)\(e\left(\frac{263}{420}\right)\)\(e\left(\frac{69}{140}\right)\)\(e\left(\frac{13}{105}\right)\)\(e\left(\frac{89}{840}\right)\)\(e\left(\frac{11}{280}\right)\)\(e\left(\frac{104}{105}\right)\)\(e\left(\frac{179}{840}\right)\)\(e\left(\frac{1}{120}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6027 }(872,a) \;\) at \(\;a = \) e.g. 2