Properties

Label 6018.4591
Modulus $6018$
Conductor $59$
Order $29$
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(58))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,54]))
 
pari: [g,chi] = znchar(Mod(4591,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(59\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(29\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{59}(48,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.u

\(\chi_{6018}(205,\cdot)\) \(\chi_{6018}(307,\cdot)\) \(\chi_{6018}(715,\cdot)\) \(\chi_{6018}(1225,\cdot)\) \(\chi_{6018}(1327,\cdot)\) \(\chi_{6018}(1939,\cdot)\) \(\chi_{6018}(2041,\cdot)\) \(\chi_{6018}(2143,\cdot)\) \(\chi_{6018}(2245,\cdot)\) \(\chi_{6018}(2347,\cdot)\) \(\chi_{6018}(2653,\cdot)\) \(\chi_{6018}(2755,\cdot)\) \(\chi_{6018}(2857,\cdot)\) \(\chi_{6018}(2959,\cdot)\) \(\chi_{6018}(3163,\cdot)\) \(\chi_{6018}(3265,\cdot)\) \(\chi_{6018}(3367,\cdot)\) \(\chi_{6018}(3673,\cdot)\) \(\chi_{6018}(3979,\cdot)\) \(\chi_{6018}(4183,\cdot)\) \(\chi_{6018}(4387,\cdot)\) \(\chi_{6018}(4489,\cdot)\) \(\chi_{6018}(4591,\cdot)\) \(\chi_{6018}(4795,\cdot)\) \(\chi_{6018}(5101,\cdot)\) \(\chi_{6018}(5509,\cdot)\) \(\chi_{6018}(5713,\cdot)\) \(\chi_{6018}(5917,\cdot)\)

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: $\Q(\zeta_{29})$
Fixed field: Number field defined by a degree 29 polynomial

Values on generators

\((4013,1771,1123)\) → \((1,1,e\left(\frac{27}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(4591, a) \) \(1\)\(1\)\(e\left(\frac{17}{29}\right)\)\(e\left(\frac{22}{29}\right)\)\(e\left(\frac{8}{29}\right)\)\(e\left(\frac{26}{29}\right)\)\(e\left(\frac{11}{29}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{5}{29}\right)\)\(e\left(\frac{2}{29}\right)\)\(e\left(\frac{18}{29}\right)\)\(e\left(\frac{10}{29}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(4591,a) \;\) at \(\;a = \) e.g. 2