Properties

Label 4830.17
Modulus $4830$
Conductor $2415$
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([66,33,22,42]))
 
pari: [g,chi] = znchar(Mod(17,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(2415\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2415}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.do

\(\chi_{4830}(17,\cdot)\) \(\chi_{4830}(143,\cdot)\) \(\chi_{4830}(227,\cdot)\) \(\chi_{4830}(383,\cdot)\) \(\chi_{4830}(467,\cdot)\) \(\chi_{4830}(563,\cdot)\) \(\chi_{4830}(677,\cdot)\) \(\chi_{4830}(773,\cdot)\) \(\chi_{4830}(803,\cdot)\) \(\chi_{4830}(983,\cdot)\) \(\chi_{4830}(1193,\cdot)\) \(\chi_{4830}(1307,\cdot)\) \(\chi_{4830}(1433,\cdot)\) \(\chi_{4830}(1487,\cdot)\) \(\chi_{4830}(1643,\cdot)\) \(\chi_{4830}(1907,\cdot)\) \(\chi_{4830}(1937,\cdot)\) \(\chi_{4830}(2273,\cdot)\) \(\chi_{4830}(2357,\cdot)\) \(\chi_{4830}(2453,\cdot)\) \(\chi_{4830}(2537,\cdot)\) \(\chi_{4830}(2567,\cdot)\) \(\chi_{4830}(2747,\cdot)\) \(\chi_{4830}(2777,\cdot)\) \(\chi_{4830}(2873,\cdot)\) \(\chi_{4830}(2903,\cdot)\) \(\chi_{4830}(2987,\cdot)\) \(\chi_{4830}(3323,\cdot)\) \(\chi_{4830}(3377,\cdot)\) \(\chi_{4830}(3503,\cdot)\) ...

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

\((3221,967,2761,1891)\) → \((-1,i,e\left(\frac{1}{6}\right),e\left(\frac{7}{22}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{31}{44}\right)\)\(e\left(\frac{19}{132}\right)\)\(e\left(\frac{7}{66}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{5}{66}\right)\)\(e\left(\frac{35}{132}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{7}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(17,a) \;\) at \(\;a = \) e.g. 2