Properties

Label 4800.121
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([0,25,0,24]))
 
pari: [g,chi] = znchar(Mod(121,4800))
 

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 \(\chi_{800}(21,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4800.eq

\(\chi_{4800}(121,\cdot)\) \(\chi_{4800}(361,\cdot)\) \(\chi_{4800}(841,\cdot)\) \(\chi_{4800}(1081,\cdot)\) \(\chi_{4800}(1321,\cdot)\) \(\chi_{4800}(1561,\cdot)\) \(\chi_{4800}(2041,\cdot)\) \(\chi_{4800}(2281,\cdot)\) \(\chi_{4800}(2521,\cdot)\) \(\chi_{4800}(2761,\cdot)\) \(\chi_{4800}(3241,\cdot)\) \(\chi_{4800}(3481,\cdot)\) \(\chi_{4800}(3721,\cdot)\) \(\chi_{4800}(3961,\cdot)\) \(\chi_{4800}(4441,\cdot)\) \(\chi_{4800}(4681,\cdot)\)

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: Number field defined by a degree 40 polynomial

Values on generators

\((4351,901,1601,577)\) → \((1,e\left(\frac{5}{8}\right),1,e\left(\frac{3}{5}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4800 }(121, a) \) \(1\)\(1\)\(i\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{3}{20}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4800 }(121,a) \;\) at \(\;a = \) e.g. 2