Properties

Label 4830.233
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([66,99,44,96]))
 
pari: [g,chi] = znchar(Mod(233,4830))
 

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 \(\chi_{2415}(233,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.dk

\(\chi_{4830}(233,\cdot)\) \(\chi_{4830}(317,\cdot)\) \(\chi_{4830}(347,\cdot)\) \(\chi_{4830}(443,\cdot)\) \(\chi_{4830}(473,\cdot)\) \(\chi_{4830}(653,\cdot)\) \(\chi_{4830}(683,\cdot)\) \(\chi_{4830}(767,\cdot)\) \(\chi_{4830}(863,\cdot)\) \(\chi_{4830}(947,\cdot)\) \(\chi_{4830}(1283,\cdot)\) \(\chi_{4830}(1313,\cdot)\) \(\chi_{4830}(1577,\cdot)\) \(\chi_{4830}(1733,\cdot)\) \(\chi_{4830}(1787,\cdot)\) \(\chi_{4830}(1913,\cdot)\) \(\chi_{4830}(2027,\cdot)\) \(\chi_{4830}(2237,\cdot)\) \(\chi_{4830}(2417,\cdot)\) \(\chi_{4830}(2447,\cdot)\) \(\chi_{4830}(2543,\cdot)\) \(\chi_{4830}(2657,\cdot)\) \(\chi_{4830}(2753,\cdot)\) \(\chi_{4830}(2837,\cdot)\) \(\chi_{4830}(2993,\cdot)\) \(\chi_{4830}(3077,\cdot)\) \(\chi_{4830}(3203,\cdot)\) \(\chi_{4830}(3383,\cdot)\) \(\chi_{4830}(3413,\cdot)\) \(\chi_{4830}(3623,\cdot)\) ...

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

\((3221,967,2761,1891)\) → \((-1,-i,e\left(\frac{1}{3}\right),e\left(\frac{8}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{89}{132}\right)\)\(e\left(\frac{5}{66}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{91}{132}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{11}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(233,a) \;\) at \(\;a = \) e.g. 2