Properties

Label 6027.2458
Modulus $6027$
Conductor $2009$
Order $140$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(140))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,120,21]))
 
pari: [g,chi] = znchar(Mod(2458,6027))
 

Basic properties

Modulus: \(6027\)
Conductor: \(2009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(140\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2009}(449,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6027.dx

\(\chi_{6027}(43,\cdot)\) \(\chi_{6027}(169,\cdot)\) \(\chi_{6027}(484,\cdot)\) \(\chi_{6027}(610,\cdot)\) \(\chi_{6027}(799,\cdot)\) \(\chi_{6027}(841,\cdot)\) \(\chi_{6027}(904,\cdot)\) \(\chi_{6027}(1156,\cdot)\) \(\chi_{6027}(1345,\cdot)\) \(\chi_{6027}(1597,\cdot)\) \(\chi_{6027}(1660,\cdot)\) \(\chi_{6027}(1702,\cdot)\) \(\chi_{6027}(1891,\cdot)\) \(\chi_{6027}(2017,\cdot)\) \(\chi_{6027}(2332,\cdot)\) \(\chi_{6027}(2458,\cdot)\) \(\chi_{6027}(2521,\cdot)\) \(\chi_{6027}(2563,\cdot)\) \(\chi_{6027}(2626,\cdot)\) \(\chi_{6027}(2752,\cdot)\) \(\chi_{6027}(2878,\cdot)\) \(\chi_{6027}(3067,\cdot)\) \(\chi_{6027}(3193,\cdot)\) \(\chi_{6027}(3319,\cdot)\) \(\chi_{6027}(3424,\cdot)\) \(\chi_{6027}(3487,\cdot)\) \(\chi_{6027}(3613,\cdot)\) \(\chi_{6027}(3739,\cdot)\) \(\chi_{6027}(3928,\cdot)\) \(\chi_{6027}(4054,\cdot)\) ...

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: $\Q(\zeta_{140})$
Fixed field: Number field defined by a degree 140 polynomial (not computed)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{6}{7}\right),e\left(\frac{3}{20}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 6027 }(2458, a) \) \(1\)\(1\)\(e\left(\frac{13}{70}\right)\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{11}{70}\right)\)\(e\left(\frac{39}{70}\right)\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{103}{140}\right)\)\(e\left(\frac{131}{140}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{53}{140}\right)\)\(e\left(\frac{7}{20}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6027 }(2458,a) \;\) at \(\;a = \) e.g. 2