Properties

Label 6018.1505
Modulus $6018$
Conductor $3009$
Order $232$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(232))
 
M = H._module
 
chi = DirichletCharacter(H, M([116,29,228]))
 
pari: [g,chi] = znchar(Mod(1505,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(3009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(232\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3009}(1505,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bh

\(\chi_{6018}(77,\cdot)\) \(\chi_{6018}(83,\cdot)\) \(\chi_{6018}(155,\cdot)\) \(\chi_{6018}(161,\cdot)\) \(\chi_{6018}(179,\cdot)\) \(\chi_{6018}(185,\cdot)\) \(\chi_{6018}(365,\cdot)\) \(\chi_{6018}(467,\cdot)\) \(\chi_{6018}(485,\cdot)\) \(\chi_{6018}(563,\cdot)\) \(\chi_{6018}(569,\cdot)\) \(\chi_{6018}(587,\cdot)\) \(\chi_{6018}(689,\cdot)\) \(\chi_{6018}(773,\cdot)\) \(\chi_{6018}(791,\cdot)\) \(\chi_{6018}(797,\cdot)\) \(\chi_{6018}(869,\cdot)\) \(\chi_{6018}(893,\cdot)\) \(\chi_{6018}(899,\cdot)\) \(\chi_{6018}(977,\cdot)\) \(\chi_{6018}(1073,\cdot)\) \(\chi_{6018}(1175,\cdot)\) \(\chi_{6018}(1277,\cdot)\) \(\chi_{6018}(1283,\cdot)\) \(\chi_{6018}(1409,\cdot)\) \(\chi_{6018}(1481,\cdot)\) \(\chi_{6018}(1505,\cdot)\) \(\chi_{6018}(1589,\cdot)\) \(\chi_{6018}(1607,\cdot)\) \(\chi_{6018}(1685,\cdot)\) ...

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: $\Q(\zeta_{232})$
Fixed field: Number field defined by a degree 232 polynomial (not computed)

Values on generators

\((4013,1771,1123)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{57}{58}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(1505, a) \) \(1\)\(1\)\(e\left(\frac{5}{232}\right)\)\(e\left(\frac{15}{232}\right)\)\(e\left(\frac{219}{232}\right)\)\(e\left(\frac{21}{29}\right)\)\(e\left(\frac{11}{116}\right)\)\(e\left(\frac{27}{232}\right)\)\(e\left(\frac{5}{116}\right)\)\(e\left(\frac{149}{232}\right)\)\(e\left(\frac{65}{232}\right)\)\(e\left(\frac{5}{58}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(1505,a) \;\) at \(\;a = \) e.g. 2