Properties

Label 6017.4914
Modulus $6017$
Conductor $6017$
Order $70$
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(70))
 
M = H._module
 
chi = DirichletCharacter(H, M([21,5]))
 
pari: [g,chi] = znchar(Mod(4914,6017))
 

Basic properties

Modulus: \(6017\)
Conductor: \(6017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(70\)
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.bh

\(\chi_{6017}(365,\cdot)\) \(\chi_{6017}(574,\cdot)\) \(\chi_{6017}(1085,\cdot)\) \(\chi_{6017}(1097,\cdot)\) \(\chi_{6017}(1337,\cdot)\) \(\chi_{6017}(1459,\cdot)\) \(\chi_{6017}(1668,\cdot)\) \(\chi_{6017}(2107,\cdot)\) \(\chi_{6017}(2191,\cdot)\) \(\chi_{6017}(2978,\cdot)\) \(\chi_{6017}(3273,\cdot)\) \(\chi_{6017}(3285,\cdot)\) \(\chi_{6017}(3647,\cdot)\) \(\chi_{6017}(3748,\cdot)\) \(\chi_{6017}(3856,\cdot)\) \(\chi_{6017}(4072,\cdot)\) \(\chi_{6017}(4842,\cdot)\) \(\chi_{6017}(4914,\cdot)\) \(\chi_{6017}(5166,\cdot)\) \(\chi_{6017}(5288,\cdot)\) \(\chi_{6017}(5473,\cdot)\) \(\chi_{6017}(5497,\cdot)\) \(\chi_{6017}(5936,\cdot)\) \(\chi_{6017}(6008,\cdot)\)

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: $\Q(\zeta_{35})$
Fixed field: Number field defined by a degree 70 polynomial

Values on generators

\((3830,2190)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{14}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\( \chi_{ 6017 }(4914, a) \) \(1\)\(1\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{3}{70}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{69}{70}\right)\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{4}{35}\right)\)\(e\left(\frac{3}{35}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{11}{14}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6017 }(4914,a) \;\) at \(\;a = \) e.g. 2