Properties

Label 4830.41
Modulus $4830$
Conductor $483$
Order $22$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4830, base_ring=CyclotomicField(22))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([11,0,11,12]))
 
pari: [g,chi] = znchar(Mod(41,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(483\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{483}(41,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.cl

\(\chi_{4830}(41,\cdot)\) \(\chi_{4830}(671,\cdot)\) \(\chi_{4830}(1301,\cdot)\) \(\chi_{4830}(1511,\cdot)\) \(\chi_{4830}(2141,\cdot)\) \(\chi_{4830}(2561,\cdot)\) \(\chi_{4830}(3821,\cdot)\) \(\chi_{4830}(4031,\cdot)\) \(\chi_{4830}(4241,\cdot)\) \(\chi_{4830}(4451,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{11})\)
Fixed field: 22.22.601130775140836298755595442714814879781421.1

Values on generators

\((3221,967,2761,1891)\) → \((-1,1,-1,e\left(\frac{6}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(41,a) \;\) at \(\;a = \) e.g. 2