Properties

Label 6027.2608
Modulus $6027$
Conductor $2009$
Order $210$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(210))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,200,21]))
 
pari: [g,chi] = znchar(Mod(2608,6027))
 

Basic properties

Modulus: \(6027\)
Conductor: \(2009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(210\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2009}(599,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6027.ef

\(\chi_{6027}(4,\cdot)\) \(\chi_{6027}(25,\cdot)\) \(\chi_{6027}(277,\cdot)\) \(\chi_{6027}(310,\cdot)\) \(\chi_{6027}(394,\cdot)\) \(\chi_{6027}(646,\cdot)\) \(\chi_{6027}(865,\cdot)\) \(\chi_{6027}(886,\cdot)\) \(\chi_{6027}(1138,\cdot)\) \(\chi_{6027}(1171,\cdot)\) \(\chi_{6027}(1234,\cdot)\) \(\chi_{6027}(1507,\cdot)\) \(\chi_{6027}(1663,\cdot)\) \(\chi_{6027}(1726,\cdot)\) \(\chi_{6027}(1747,\cdot)\) \(\chi_{6027}(1999,\cdot)\) \(\chi_{6027}(2032,\cdot)\) \(\chi_{6027}(2095,\cdot)\) \(\chi_{6027}(2116,\cdot)\) \(\chi_{6027}(2368,\cdot)\) \(\chi_{6027}(2524,\cdot)\) \(\chi_{6027}(2587,\cdot)\) \(\chi_{6027}(2608,\cdot)\) \(\chi_{6027}(2893,\cdot)\) \(\chi_{6027}(2956,\cdot)\) \(\chi_{6027}(2977,\cdot)\) \(\chi_{6027}(3229,\cdot)\) \(\chi_{6027}(3385,\cdot)\) \(\chi_{6027}(3469,\cdot)\) \(\chi_{6027}(3721,\cdot)\) ...

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: $\Q(\zeta_{105})$
Fixed field: Number field defined by a degree 210 polynomial (not computed)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{20}{21}\right),e\left(\frac{1}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 6027 }(2608, a) \) \(1\)\(1\)\(e\left(\frac{38}{105}\right)\)\(e\left(\frac{76}{105}\right)\)\(e\left(\frac{86}{105}\right)\)\(e\left(\frac{3}{35}\right)\)\(e\left(\frac{19}{105}\right)\)\(e\left(\frac{83}{210}\right)\)\(e\left(\frac{37}{70}\right)\)\(e\left(\frac{47}{105}\right)\)\(e\left(\frac{23}{210}\right)\)\(e\left(\frac{7}{30}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6027 }(2608,a) \;\) at \(\;a = \) e.g. 2