Properties

Label 6018.2843
Modulus $6018$
Conductor $3009$
Order $116$
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(6018, base_ring=CyclotomicField(116))
 
M = H._module
 
chi = DirichletCharacter(H, M([58,87,50]))
 
pari: [g,chi] = znchar(Mod(2843,6018))
 

Basic properties

Modulus: \(6018\)
Conductor: \(3009\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(116\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3009}(2843,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6018.bf

\(\chi_{6018}(47,\cdot)\) \(\chi_{6018}(89,\cdot)\) \(\chi_{6018}(149,\cdot)\) \(\chi_{6018}(191,\cdot)\) \(\chi_{6018}(455,\cdot)\) \(\chi_{6018}(659,\cdot)\) \(\chi_{6018}(701,\cdot)\) \(\chi_{6018}(863,\cdot)\) \(\chi_{6018}(1109,\cdot)\) \(\chi_{6018}(1211,\cdot)\) \(\chi_{6018}(1271,\cdot)\) \(\chi_{6018}(1517,\cdot)\) \(\chi_{6018}(1577,\cdot)\) \(\chi_{6018}(1721,\cdot)\) \(\chi_{6018}(1781,\cdot)\) \(\chi_{6018}(1883,\cdot)\) \(\chi_{6018}(1925,\cdot)\) \(\chi_{6018}(1985,\cdot)\) \(\chi_{6018}(2189,\cdot)\) \(\chi_{6018}(2333,\cdot)\) \(\chi_{6018}(2393,\cdot)\) \(\chi_{6018}(2639,\cdot)\) \(\chi_{6018}(2699,\cdot)\) \(\chi_{6018}(2843,\cdot)\) \(\chi_{6018}(2945,\cdot)\) \(\chi_{6018}(3005,\cdot)\) \(\chi_{6018}(3047,\cdot)\) \(\chi_{6018}(3107,\cdot)\) \(\chi_{6018}(3209,\cdot)\) \(\chi_{6018}(3251,\cdot)\) ...

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: $\Q(\zeta_{116})$
Fixed field: Number field defined by a degree 116 polynomial (not computed)

Values on generators

\((4013,1771,1123)\) → \((-1,-i,e\left(\frac{25}{58}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6018 }(2843, a) \) \(1\)\(1\)\(e\left(\frac{97}{116}\right)\)\(e\left(\frac{1}{116}\right)\)\(e\left(\frac{61}{116}\right)\)\(e\left(\frac{23}{58}\right)\)\(e\left(\frac{51}{58}\right)\)\(e\left(\frac{25}{116}\right)\)\(e\left(\frac{39}{58}\right)\)\(e\left(\frac{37}{116}\right)\)\(e\left(\frac{101}{116}\right)\)\(e\left(\frac{49}{58}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6018 }(2843,a) \;\) at \(\;a = \) e.g. 2