Properties

Label 4800.487
Modulus $4800$
Conductor $800$
Order $40$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4800, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([20,5,0,18]))
 
pari: [g,chi] = znchar(Mod(487,4800))
 

Basic properties

Modulus: \(4800\)
Conductor: \(800\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{800}(187,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4800.ev

\(\chi_{4800}(487,\cdot)\) \(\chi_{4800}(823,\cdot)\) \(\chi_{4800}(967,\cdot)\) \(\chi_{4800}(1303,\cdot)\) \(\chi_{4800}(1447,\cdot)\) \(\chi_{4800}(1783,\cdot)\) \(\chi_{4800}(1927,\cdot)\) \(\chi_{4800}(2263,\cdot)\) \(\chi_{4800}(2887,\cdot)\) \(\chi_{4800}(3223,\cdot)\) \(\chi_{4800}(3367,\cdot)\) \(\chi_{4800}(3703,\cdot)\) \(\chi_{4800}(3847,\cdot)\) \(\chi_{4800}(4183,\cdot)\) \(\chi_{4800}(4327,\cdot)\) \(\chi_{4800}(4663,\cdot)\)

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: \(\Q(\zeta_{40})\)
Fixed field: 40.40.386856262276681335905976320000000000000000000000000000000000000000000000000000000000000000000000.1

Values on generators

\((4351,901,1601,577)\) → \((-1,e\left(\frac{1}{8}\right),1,e\left(\frac{9}{20}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4800 }(487, a) \) \(1\)\(1\)\(1\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{11}{20}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4800 }(487,a) \;\) at \(\;a = \) e.g. 2