Properties

Label 6018.617
Modulus $6018$
Conductor $3009$
Order $464$
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(464))
 
M = H._module
 
chi = DirichletCharacter(H, M([232,145,272]))
 
pari: [g,chi] = znchar(Mod(617,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(3009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(464\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3009}(617,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bn

\(\chi_{6018}(5,\cdot)\) \(\chi_{6018}(29,\cdot)\) \(\chi_{6018}(41,\cdot)\) \(\chi_{6018}(71,\cdot)\) \(\chi_{6018}(95,\cdot)\) \(\chi_{6018}(107,\cdot)\) \(\chi_{6018}(125,\cdot)\) \(\chi_{6018}(143,\cdot)\) \(\chi_{6018}(167,\cdot)\) \(\chi_{6018}(197,\cdot)\) \(\chi_{6018}(245,\cdot)\) \(\chi_{6018}(299,\cdot)\) \(\chi_{6018}(311,\cdot)\) \(\chi_{6018}(317,\cdot)\) \(\chi_{6018}(371,\cdot)\) \(\chi_{6018}(449,\cdot)\) \(\chi_{6018}(479,\cdot)\) \(\chi_{6018}(521,\cdot)\) \(\chi_{6018}(551,\cdot)\) \(\chi_{6018}(605,\cdot)\) \(\chi_{6018}(617,\cdot)\) \(\chi_{6018}(635,\cdot)\) \(\chi_{6018}(641,\cdot)\) \(\chi_{6018}(653,\cdot)\) \(\chi_{6018}(677,\cdot)\) \(\chi_{6018}(725,\cdot)\) \(\chi_{6018}(737,\cdot)\) \(\chi_{6018}(743,\cdot)\) \(\chi_{6018}(779,\cdot)\) \(\chi_{6018}(845,\cdot)\) ...

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

\((4013,1771,1123)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{17}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(617, a) \) \(1\)\(1\)\(e\left(\frac{269}{464}\right)\)\(e\left(\frac{459}{464}\right)\)\(e\left(\frac{159}{464}\right)\)\(e\left(\frac{73}{116}\right)\)\(e\left(\frac{151}{232}\right)\)\(e\left(\frac{455}{464}\right)\)\(e\left(\frac{37}{232}\right)\)\(e\left(\frac{453}{464}\right)\)\(e\left(\frac{249}{464}\right)\)\(e\left(\frac{33}{58}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(617,a) \;\) at \(\;a = \) e.g. 2