Properties

Label 6017.260
Modulus $6017$
Conductor $6017$
Order $2730$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(2730))
 
M = H._module
 
chi = DirichletCharacter(H, M([1911,2335]))
 
pari: [g,chi] = znchar(Mod(260,6017))
 

Basic properties

Modulus: \(6017\)
Conductor: \(6017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2730\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6017.cl

\(\chi_{6017}(2,\cdot)\) \(\chi_{6017}(7,\cdot)\) \(\chi_{6017}(17,\cdot)\) \(\chi_{6017}(18,\cdot)\) \(\chi_{6017}(50,\cdot)\) \(\chi_{6017}(57,\cdot)\) \(\chi_{6017}(61,\cdot)\) \(\chi_{6017}(63,\cdot)\) \(\chi_{6017}(95,\cdot)\) \(\chi_{6017}(112,\cdot)\) \(\chi_{6017}(134,\cdot)\) \(\chi_{6017}(162,\cdot)\) \(\chi_{6017}(200,\cdot)\) \(\chi_{6017}(211,\cdot)\) \(\chi_{6017}(228,\cdot)\) \(\chi_{6017}(260,\cdot)\) \(\chi_{6017}(271,\cdot)\) \(\chi_{6017}(272,\cdot)\) \(\chi_{6017}(281,\cdot)\) \(\chi_{6017}(283,\cdot)\) \(\chi_{6017}(288,\cdot)\) \(\chi_{6017}(337,\cdot)\) \(\chi_{6017}(354,\cdot)\) \(\chi_{6017}(358,\cdot)\) \(\chi_{6017}(359,\cdot)\) \(\chi_{6017}(370,\cdot)\) \(\chi_{6017}(371,\cdot)\) \(\chi_{6017}(376,\cdot)\) \(\chi_{6017}(381,\cdot)\) \(\chi_{6017}(387,\cdot)\) ...

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: $\Q(\zeta_{1365})$
Fixed field: Number field defined by a degree 2730 polynomial (not computed)

Values on generators

\((3830,2190)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{467}{546}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\( \chi_{ 6017 }(260, a) \) \(1\)\(1\)\(e\left(\frac{758}{1365}\right)\)\(e\left(\frac{37}{70}\right)\)\(e\left(\frac{151}{1365}\right)\)\(e\left(\frac{2459}{2730}\right)\)\(e\left(\frac{229}{2730}\right)\)\(e\left(\frac{1361}{1365}\right)\)\(e\left(\frac{303}{455}\right)\)\(e\left(\frac{2}{35}\right)\)\(e\left(\frac{83}{182}\right)\)\(e\left(\frac{349}{546}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6017 }(260,a) \;\) at \(\;a = \) e.g. 2