Properties

Label 4830.73
Modulus $4830$
Conductor $805$
Order $132$
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(132))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,99,22,24]))
 
pari: [g,chi] = znchar(Mod(73,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(805\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{805}(73,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.dr

\(\chi_{4830}(73,\cdot)\) \(\chi_{4830}(187,\cdot)\) \(\chi_{4830}(397,\cdot)\) \(\chi_{4830}(577,\cdot)\) \(\chi_{4830}(607,\cdot)\) \(\chi_{4830}(703,\cdot)\) \(\chi_{4830}(817,\cdot)\) \(\chi_{4830}(913,\cdot)\) \(\chi_{4830}(997,\cdot)\) \(\chi_{4830}(1153,\cdot)\) \(\chi_{4830}(1237,\cdot)\) \(\chi_{4830}(1363,\cdot)\) \(\chi_{4830}(1543,\cdot)\) \(\chi_{4830}(1573,\cdot)\) \(\chi_{4830}(1783,\cdot)\) \(\chi_{4830}(1867,\cdot)\) \(\chi_{4830}(1963,\cdot)\) \(\chi_{4830}(2203,\cdot)\) \(\chi_{4830}(2257,\cdot)\) \(\chi_{4830}(2467,\cdot)\) \(\chi_{4830}(2497,\cdot)\) \(\chi_{4830}(2677,\cdot)\) \(\chi_{4830}(2707,\cdot)\) \(\chi_{4830}(2833,\cdot)\) \(\chi_{4830}(2887,\cdot)\) \(\chi_{4830}(3223,\cdot)\) \(\chi_{4830}(3307,\cdot)\) \(\chi_{4830}(3337,\cdot)\) \(\chi_{4830}(3433,\cdot)\) \(\chi_{4830}(3463,\cdot)\) ...

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: $\Q(\zeta_{132})$
Fixed field: Number field defined by a degree 132 polynomial (not computed)

Values on generators

\((3221,967,2761,1891)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{2}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{25}{132}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{119}{132}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{7}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(73,a) \;\) at \(\;a = \) e.g. 2