Properties

Label 6018.7
Modulus $6018$
Conductor $1003$
Order $464$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(464))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,319,144]))
 
pari: [g,chi] = znchar(Mod(7,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(1003\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(464\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1003}(7,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bl

\(\chi_{6018}(7,\cdot)\) \(\chi_{6018}(79,\cdot)\) \(\chi_{6018}(133,\cdot)\) \(\chi_{6018}(139,\cdot)\) \(\chi_{6018}(163,\cdot)\) \(\chi_{6018}(175,\cdot)\) \(\chi_{6018}(181,\cdot)\) \(\chi_{6018}(193,\cdot)\) \(\chi_{6018}(199,\cdot)\) \(\chi_{6018}(241,\cdot)\) \(\chi_{6018}(265,\cdot)\) \(\chi_{6018}(277,\cdot)\) \(\chi_{6018}(343,\cdot)\) \(\chi_{6018}(379,\cdot)\) \(\chi_{6018}(403,\cdot)\) \(\chi_{6018}(439,\cdot)\) \(\chi_{6018}(481,\cdot)\) \(\chi_{6018}(487,\cdot)\) \(\chi_{6018}(499,\cdot)\) \(\chi_{6018}(517,\cdot)\) \(\chi_{6018}(547,\cdot)\) \(\chi_{6018}(607,\cdot)\) \(\chi_{6018}(619,\cdot)\) \(\chi_{6018}(643,\cdot)\) \(\chi_{6018}(685,\cdot)\) \(\chi_{6018}(787,\cdot)\) \(\chi_{6018}(793,\cdot)\) \(\chi_{6018}(847,\cdot)\) \(\chi_{6018}(853,\cdot)\) \(\chi_{6018}(877,\cdot)\) ...

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: $\Q(\zeta_{464})$
Fixed field: Number field defined by a degree 464 polynomial (not computed)

Values on generators

\((4013,1771,1123)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{9}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(7, a) \) \(-1\)\(1\)\(e\left(\frac{139}{464}\right)\)\(e\left(\frac{69}{464}\right)\)\(e\left(\frac{265}{464}\right)\)\(e\left(\frac{83}{116}\right)\)\(e\left(\frac{97}{232}\right)\)\(e\left(\frac{449}{464}\right)\)\(e\left(\frac{139}{232}\right)\)\(e\left(\frac{291}{464}\right)\)\(e\left(\frac{183}{464}\right)\)\(e\left(\frac{13}{29}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(7,a) \;\) at \(\;a = \) e.g. 2