Properties

Label 4830.19
Modulus $4830$
Conductor $805$
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([0,33,55,45]))
 
pari: [g,chi] = znchar(Mod(19,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(805\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{805}(19,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.cx

\(\chi_{4830}(19,\cdot)\) \(\chi_{4830}(199,\cdot)\) \(\chi_{4830}(619,\cdot)\) \(\chi_{4830}(649,\cdot)\) \(\chi_{4830}(1069,\cdot)\) \(\chi_{4830}(1249,\cdot)\) \(\chi_{4830}(1279,\cdot)\) \(\chi_{4830}(1459,\cdot)\) \(\chi_{4830}(1489,\cdot)\) \(\chi_{4830}(1699,\cdot)\) \(\chi_{4830}(2089,\cdot)\) \(\chi_{4830}(2719,\cdot)\) \(\chi_{4830}(2959,\cdot)\) \(\chi_{4830}(3139,\cdot)\) \(\chi_{4830}(3349,\cdot)\) \(\chi_{4830}(3379,\cdot)\) \(\chi_{4830}(3559,\cdot)\) \(\chi_{4830}(3769,\cdot)\) \(\chi_{4830}(4009,\cdot)\) \(\chi_{4830}(4219,\cdot)\)

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

\((3221,967,2761,1891)\) → \((1,-1,e\left(\frac{5}{6}\right),e\left(\frac{15}{22}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{7}{66}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{2}{3}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(19,a) \;\) at \(\;a = \) e.g. 2