Properties

Label 4830.61
Modulus $4830$
Conductor $161$
Order $66$
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(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,55,51]))
 
pari: [g,chi] = znchar(Mod(61,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(161\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{161}(61,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.db

\(\chi_{4830}(61,\cdot)\) \(\chi_{4830}(241,\cdot)\) \(\chi_{4830}(451,\cdot)\) \(\chi_{4830}(481,\cdot)\) \(\chi_{4830}(661,\cdot)\) \(\chi_{4830}(871,\cdot)\) \(\chi_{4830}(1111,\cdot)\) \(\chi_{4830}(1321,\cdot)\) \(\chi_{4830}(1951,\cdot)\) \(\chi_{4830}(2131,\cdot)\) \(\chi_{4830}(2551,\cdot)\) \(\chi_{4830}(2581,\cdot)\) \(\chi_{4830}(3001,\cdot)\) \(\chi_{4830}(3181,\cdot)\) \(\chi_{4830}(3211,\cdot)\) \(\chi_{4830}(3391,\cdot)\) \(\chi_{4830}(3421,\cdot)\) \(\chi_{4830}(3631,\cdot)\) \(\chi_{4830}(4021,\cdot)\) \(\chi_{4830}(4651,\cdot)\)

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: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 66 polynomial

Values on generators

\((3221,967,2761,1891)\) → \((1,1,e\left(\frac{5}{6}\right),e\left(\frac{17}{22}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{25}{33}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{1}{6}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(61,a) \;\) at \(\;a = \) e.g. 2