Properties

Label 4830.101
Modulus $4830$
Conductor $483$
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([33,0,11,30]))
 
pari: [g,chi] = znchar(Mod(101,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(483\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{483}(101,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.da

\(\chi_{4830}(101,\cdot)\) \(\chi_{4830}(131,\cdot)\) \(\chi_{4830}(311,\cdot)\) \(\chi_{4830}(731,\cdot)\) \(\chi_{4830}(761,\cdot)\) \(\chi_{4830}(1181,\cdot)\) \(\chi_{4830}(1361,\cdot)\) \(\chi_{4830}(1991,\cdot)\) \(\chi_{4830}(2201,\cdot)\) \(\chi_{4830}(2441,\cdot)\) \(\chi_{4830}(2651,\cdot)\) \(\chi_{4830}(2831,\cdot)\) \(\chi_{4830}(2861,\cdot)\) \(\chi_{4830}(3071,\cdot)\) \(\chi_{4830}(3251,\cdot)\) \(\chi_{4830}(3491,\cdot)\) \(\chi_{4830}(4121,\cdot)\) \(\chi_{4830}(4511,\cdot)\) \(\chi_{4830}(4721,\cdot)\) \(\chi_{4830}(4751,\cdot)\)

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

\((3221,967,2761,1891)\) → \((-1,1,e\left(\frac{1}{6}\right),e\left(\frac{5}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{43}{66}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{1}{3}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(101,a) \;\) at \(\;a = \) e.g. 2