Properties

Label 6027.848
Modulus $6027$
Conductor $6027$
Order $280$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(280))
 
M = H._module
 
chi = DirichletCharacter(H, M([140,200,77]))
 
pari: [g,chi] = znchar(Mod(848,6027))
 

Basic properties

Modulus: \(6027\)
Conductor: \(6027\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(280\)
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 6027.ep

\(\chi_{6027}(29,\cdot)\) \(\chi_{6027}(71,\cdot)\) \(\chi_{6027}(134,\cdot)\) \(\chi_{6027}(176,\cdot)\) \(\chi_{6027}(218,\cdot)\) \(\chi_{6027}(239,\cdot)\) \(\chi_{6027}(281,\cdot)\) \(\chi_{6027}(302,\cdot)\) \(\chi_{6027}(386,\cdot)\) \(\chi_{6027}(470,\cdot)\) \(\chi_{6027}(596,\cdot)\) \(\chi_{6027}(680,\cdot)\) \(\chi_{6027}(764,\cdot)\) \(\chi_{6027}(827,\cdot)\) \(\chi_{6027}(848,\cdot)\) \(\chi_{6027}(890,\cdot)\) \(\chi_{6027}(995,\cdot)\) \(\chi_{6027}(1037,\cdot)\) \(\chi_{6027}(1100,\cdot)\) \(\chi_{6027}(1142,\cdot)\) \(\chi_{6027}(1163,\cdot)\) \(\chi_{6027}(1247,\cdot)\) \(\chi_{6027}(1331,\cdot)\) \(\chi_{6027}(1457,\cdot)\) \(\chi_{6027}(1541,\cdot)\) \(\chi_{6027}(1625,\cdot)\) \(\chi_{6027}(1646,\cdot)\) \(\chi_{6027}(1688,\cdot)\) \(\chi_{6027}(1709,\cdot)\) \(\chi_{6027}(1751,\cdot)\) ...

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: $\Q(\zeta_{280})$
Fixed field: Number field defined by a degree 280 polynomial (not computed)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{11}{40}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 6027 }(848, a) \) \(1\)\(1\)\(e\left(\frac{31}{140}\right)\)\(e\left(\frac{31}{70}\right)\)\(e\left(\frac{37}{140}\right)\)\(e\left(\frac{93}{140}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{251}{280}\right)\)\(e\left(\frac{27}{280}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{121}{280}\right)\)\(e\left(\frac{19}{40}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6027 }(848,a) \;\) at \(\;a = \) e.g. 2