Properties

Label 6017.467
Modulus $6017$
Conductor $6017$
Order $455$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(910))
 
M = H._module
 
chi = DirichletCharacter(H, M([364,760]))
 
pari: [g,chi] = znchar(Mod(467,6017))
 

Basic properties

Modulus: \(6017\)
Conductor: \(6017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(455\)
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 6017.cb

\(\chi_{6017}(64,\cdot)\) \(\chi_{6017}(93,\cdot)\) \(\chi_{6017}(114,\cdot)\) \(\chi_{6017}(179,\cdot)\) \(\chi_{6017}(185,\cdot)\) \(\chi_{6017}(212,\cdot)\) \(\chi_{6017}(218,\cdot)\) \(\chi_{6017}(224,\cdot)\) \(\chi_{6017}(240,\cdot)\) \(\chi_{6017}(247,\cdot)\) \(\chi_{6017}(267,\cdot)\) \(\chi_{6017}(268,\cdot)\) \(\chi_{6017}(290,\cdot)\) \(\chi_{6017}(295,\cdot)\) \(\chi_{6017}(311,\cdot)\) \(\chi_{6017}(355,\cdot)\) \(\chi_{6017}(383,\cdot)\) \(\chi_{6017}(399,\cdot)\) \(\chi_{6017}(422,\cdot)\) \(\chi_{6017}(444,\cdot)\) \(\chi_{6017}(449,\cdot)\) \(\chi_{6017}(460,\cdot)\) \(\chi_{6017}(467,\cdot)\) \(\chi_{6017}(482,\cdot)\) \(\chi_{6017}(576,\cdot)\) \(\chi_{6017}(599,\cdot)\) \(\chi_{6017}(631,\cdot)\) \(\chi_{6017}(632,\cdot)\) \(\chi_{6017}(647,\cdot)\) \(\chi_{6017}(696,\cdot)\) ...

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: $\Q(\zeta_{455})$
Fixed field: Number field defined by a degree 455 polynomial (not computed)

Values on generators

\((3830,2190)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{76}{91}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\( \chi_{ 6017 }(467, a) \) \(1\)\(1\)\(e\left(\frac{107}{455}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{214}{455}\right)\)\(e\left(\frac{43}{455}\right)\)\(e\left(\frac{328}{455}\right)\)\(e\left(\frac{374}{455}\right)\)\(e\left(\frac{321}{455}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{30}{91}\right)\)\(e\left(\frac{87}{91}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6017 }(467,a) \;\) at \(\;a = \) e.g. 2