Properties

Label 6336.41
Modulus $6336$
Conductor $3168$
Order $120$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6336, base_ring=CyclotomicField(120))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,105,100,36]))
 
pari: [g,chi] = znchar(Mod(41,6336))
 

Basic properties

Modulus: \(6336\)
Conductor: \(3168\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3168}(1229,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6336.fv

\(\chi_{6336}(41,\cdot)\) \(\chi_{6336}(281,\cdot)\) \(\chi_{6336}(425,\cdot)\) \(\chi_{6336}(569,\cdot)\) \(\chi_{6336}(761,\cdot)\) \(\chi_{6336}(1289,\cdot)\) \(\chi_{6336}(1337,\cdot)\) \(\chi_{6336}(1481,\cdot)\) \(\chi_{6336}(1625,\cdot)\) \(\chi_{6336}(1865,\cdot)\) \(\chi_{6336}(2009,\cdot)\) \(\chi_{6336}(2153,\cdot)\) \(\chi_{6336}(2345,\cdot)\) \(\chi_{6336}(2873,\cdot)\) \(\chi_{6336}(2921,\cdot)\) \(\chi_{6336}(3065,\cdot)\) \(\chi_{6336}(3209,\cdot)\) \(\chi_{6336}(3449,\cdot)\) \(\chi_{6336}(3593,\cdot)\) \(\chi_{6336}(3737,\cdot)\) \(\chi_{6336}(3929,\cdot)\) \(\chi_{6336}(4457,\cdot)\) \(\chi_{6336}(4505,\cdot)\) \(\chi_{6336}(4649,\cdot)\) \(\chi_{6336}(4793,\cdot)\) \(\chi_{6336}(5033,\cdot)\) \(\chi_{6336}(5177,\cdot)\) \(\chi_{6336}(5321,\cdot)\) \(\chi_{6336}(5513,\cdot)\) \(\chi_{6336}(6041,\cdot)\) ...

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: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((4159,4357,3521,1729)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{3}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6336 }(41, a) \) \(1\)\(1\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{11}{120}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{67}{120}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{17}{40}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6336 }(41,a) \;\) at \(\;a = \) e.g. 2