Properties

Label 6018.1069
Modulus $6018$
Conductor $1003$
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([0,87,72]))
 
pari: [g,chi] = znchar(Mod(1069,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(1003\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(232\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1003}(66,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bi

\(\chi_{6018}(19,\cdot)\) \(\chi_{6018}(25,\cdot)\) \(\chi_{6018}(49,\cdot)\) \(\chi_{6018}(121,\cdot)\) \(\chi_{6018}(127,\cdot)\) \(\chi_{6018}(145,\cdot)\) \(\chi_{6018}(223,\cdot)\) \(\chi_{6018}(253,\cdot)\) \(\chi_{6018}(331,\cdot)\) \(\chi_{6018}(433,\cdot)\) \(\chi_{6018}(529,\cdot)\) \(\chi_{6018}(535,\cdot)\) \(\chi_{6018}(553,\cdot)\) \(\chi_{6018}(559,\cdot)\) \(\chi_{6018}(631,\cdot)\) \(\chi_{6018}(661,\cdot)\) \(\chi_{6018}(733,\cdot)\) \(\chi_{6018}(757,\cdot)\) \(\chi_{6018}(835,\cdot)\) \(\chi_{6018}(841,\cdot)\) \(\chi_{6018}(961,\cdot)\) \(\chi_{6018}(1039,\cdot)\) \(\chi_{6018}(1069,\cdot)\) \(\chi_{6018}(1141,\cdot)\) \(\chi_{6018}(1147,\cdot)\) \(\chi_{6018}(1243,\cdot)\) \(\chi_{6018}(1267,\cdot)\) \(\chi_{6018}(1351,\cdot)\) \(\chi_{6018}(1369,\cdot)\) \(\chi_{6018}(1549,\cdot)\) ...

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

\((4013,1771,1123)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{9}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(1069, a) \) \(1\)\(1\)\(e\left(\frac{171}{232}\right)\)\(e\left(\frac{165}{232}\right)\)\(e\left(\frac{89}{232}\right)\)\(e\left(\frac{27}{58}\right)\)\(e\left(\frac{5}{116}\right)\)\(e\left(\frac{65}{232}\right)\)\(e\left(\frac{55}{116}\right)\)\(e\left(\frac{131}{232}\right)\)\(e\left(\frac{135}{232}\right)\)\(e\left(\frac{13}{29}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(1069,a) \;\) at \(\;a = \) e.g. 2