Properties

Label 6018.43
Modulus $6018$
Conductor $1003$
Order $232$
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(232))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,29,132]))
 
pari: [g,chi] = znchar(Mod(43,6018))
 

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 \(\chi_{1003}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bg

\(\chi_{6018}(43,\cdot)\) \(\chi_{6018}(151,\cdot)\) \(\chi_{6018}(229,\cdot)\) \(\chi_{6018}(247,\cdot)\) \(\chi_{6018}(325,\cdot)\) \(\chi_{6018}(349,\cdot)\) \(\chi_{6018}(427,\cdot)\) \(\chi_{6018}(451,\cdot)\) \(\chi_{6018}(457,\cdot)\) \(\chi_{6018}(637,\cdot)\) \(\chi_{6018}(655,\cdot)\) \(\chi_{6018}(739,\cdot)\) \(\chi_{6018}(763,\cdot)\) \(\chi_{6018}(859,\cdot)\) \(\chi_{6018}(865,\cdot)\) \(\chi_{6018}(937,\cdot)\) \(\chi_{6018}(967,\cdot)\) \(\chi_{6018}(1045,\cdot)\) \(\chi_{6018}(1165,\cdot)\) \(\chi_{6018}(1171,\cdot)\) \(\chi_{6018}(1249,\cdot)\) \(\chi_{6018}(1273,\cdot)\) \(\chi_{6018}(1345,\cdot)\) \(\chi_{6018}(1375,\cdot)\) \(\chi_{6018}(1447,\cdot)\) \(\chi_{6018}(1453,\cdot)\) \(\chi_{6018}(1471,\cdot)\) \(\chi_{6018}(1477,\cdot)\) \(\chi_{6018}(1573,\cdot)\) \(\chi_{6018}(1675,\cdot)\) ...

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

\((4013,1771,1123)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{33}{58}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(43, a) \) \(-1\)\(1\)\(e\left(\frac{9}{232}\right)\)\(e\left(\frac{143}{232}\right)\)\(e\left(\frac{23}{232}\right)\)\(e\left(\frac{3}{29}\right)\)\(e\left(\frac{43}{116}\right)\)\(e\left(\frac{95}{232}\right)\)\(e\left(\frac{9}{116}\right)\)\(e\left(\frac{129}{232}\right)\)\(e\left(\frac{1}{232}\right)\)\(e\left(\frac{19}{29}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(43,a) \;\) at \(\;a = \) e.g. 2