Properties

Label 6027.334
Modulus $6027$
Conductor $2009$
Order $840$
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(840))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,460,21]))
 
pari: [g,chi] = znchar(Mod(334,6027))
 

Basic properties

Modulus: \(6027\)
Conductor: \(2009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(840\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2009}(334,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6027.ex

\(\chi_{6027}(52,\cdot)\) \(\chi_{6027}(94,\cdot)\) \(\chi_{6027}(136,\cdot)\) \(\chi_{6027}(145,\cdot)\) \(\chi_{6027}(157,\cdot)\) \(\chi_{6027}(199,\cdot)\) \(\chi_{6027}(220,\cdot)\) \(\chi_{6027}(229,\cdot)\) \(\chi_{6027}(304,\cdot)\) \(\chi_{6027}(334,\cdot)\) \(\chi_{6027}(376,\cdot)\) \(\chi_{6027}(388,\cdot)\) \(\chi_{6027}(397,\cdot)\) \(\chi_{6027}(439,\cdot)\) \(\chi_{6027}(481,\cdot)\) \(\chi_{6027}(514,\cdot)\) \(\chi_{6027}(544,\cdot)\) \(\chi_{6027}(586,\cdot)\) \(\chi_{6027}(598,\cdot)\) \(\chi_{6027}(628,\cdot)\) \(\chi_{6027}(649,\cdot)\) \(\chi_{6027}(682,\cdot)\) \(\chi_{6027}(691,\cdot)\) \(\chi_{6027}(703,\cdot)\) \(\chi_{6027}(712,\cdot)\) \(\chi_{6027}(745,\cdot)\) \(\chi_{6027}(796,\cdot)\) \(\chi_{6027}(808,\cdot)\) \(\chi_{6027}(850,\cdot)\) \(\chi_{6027}(880,\cdot)\) ...

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

\((4019,493,2794)\) → \((1,e\left(\frac{23}{42}\right),e\left(\frac{1}{40}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 6027 }(334, a) \) \(1\)\(1\)\(e\left(\frac{373}{420}\right)\)\(e\left(\frac{163}{210}\right)\)\(e\left(\frac{181}{420}\right)\)\(e\left(\frac{93}{140}\right)\)\(e\left(\frac{67}{210}\right)\)\(e\left(\frac{823}{840}\right)\)\(e\left(\frac{237}{280}\right)\)\(e\left(\frac{58}{105}\right)\)\(e\left(\frac{433}{840}\right)\)\(e\left(\frac{47}{120}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6027 }(334,a) \;\) at \(\;a = \) e.g. 2