Properties

Label 4830.947
Modulus $4830$
Conductor $2415$
Order $132$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4830, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([66,33,44,24]))
 
pari: [g,chi] = znchar(Mod(947,4830))
 

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 \(\chi_{2415}(947,\cdot)\)
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()
 
order = charorder(g,chi)
 
[ 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

\((3221,967,2761,1891)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{2}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\( \chi_{ 4830 }(947, a) \) \(1\)\(1\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{47}{132}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{14}{33}\right)\)\(e\left(\frac{97}{132}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{5}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(947,a) \;\) at \(\;a = \) e.g. 2