Properties

Label 6017.244
Modulus $6017$
Conductor $6017$
Order $910$
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([91,395]))
 
pari: [g,chi] = znchar(Mod(244,6017))
 

Basic properties

Modulus: \(6017\)
Conductor: \(6017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(910\)
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.cf

\(\chi_{6017}(8,\cdot)\) \(\chi_{6017}(68,\cdot)\) \(\chi_{6017}(79,\cdot)\) \(\chi_{6017}(94,\cdot)\) \(\chi_{6017}(101,\cdot)\) \(\chi_{6017}(105,\cdot)\) \(\chi_{6017}(138,\cdot)\) \(\chi_{6017}(151,\cdot)\) \(\chi_{6017}(156,\cdot)\) \(\chi_{6017}(173,\cdot)\) \(\chi_{6017}(226,\cdot)\) \(\chi_{6017}(238,\cdot)\) \(\chi_{6017}(244,\cdot)\) \(\chi_{6017}(255,\cdot)\) \(\chi_{6017}(270,\cdot)\) \(\chi_{6017}(299,\cdot)\) \(\chi_{6017}(332,\cdot)\) \(\chi_{6017}(338,\cdot)\) \(\chi_{6017}(343,\cdot)\) \(\chi_{6017}(380,\cdot)\) \(\chi_{6017}(382,\cdot)\) \(\chi_{6017}(393,\cdot)\) \(\chi_{6017}(398,\cdot)\) \(\chi_{6017}(447,\cdot)\) \(\chi_{6017}(457,\cdot)\) \(\chi_{6017}(503,\cdot)\) \(\chi_{6017}(512,\cdot)\) \(\chi_{6017}(523,\cdot)\) \(\chi_{6017}(578,\cdot)\) \(\chi_{6017}(602,\cdot)\) ...

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 910 polynomial (not computed)

Values on generators

\((3830,2190)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{79}{182}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\( \chi_{ 6017 }(244, a) \) \(1\)\(1\)\(e\left(\frac{243}{455}\right)\)\(e\left(\frac{1}{70}\right)\)\(e\left(\frac{31}{455}\right)\)\(e\left(\frac{89}{910}\right)\)\(e\left(\frac{499}{910}\right)\)\(e\left(\frac{186}{455}\right)\)\(e\left(\frac{274}{455}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{115}{182}\right)\)\(e\left(\frac{15}{182}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6017 }(244,a) \;\) at \(\;a = \) e.g. 2