Properties

Label 4830.121
Modulus $4830$
Conductor $161$
Order $33$
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([0,0,22,54]))
 
pari: [g,chi] = znchar(Mod(121,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(161\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(33\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{161}(121,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.cm

\(\chi_{4830}(121,\cdot)\) \(\chi_{4830}(151,\cdot)\) \(\chi_{4830}(331,\cdot)\) \(\chi_{4830}(361,\cdot)\) \(\chi_{4830}(541,\cdot)\) \(\chi_{4830}(961,\cdot)\) \(\chi_{4830}(991,\cdot)\) \(\chi_{4830}(1411,\cdot)\) \(\chi_{4830}(1591,\cdot)\) \(\chi_{4830}(2221,\cdot)\) \(\chi_{4830}(2431,\cdot)\) \(\chi_{4830}(2671,\cdot)\) \(\chi_{4830}(2881,\cdot)\) \(\chi_{4830}(3061,\cdot)\) \(\chi_{4830}(3091,\cdot)\) \(\chi_{4830}(3301,\cdot)\) \(\chi_{4830}(3481,\cdot)\) \(\chi_{4830}(3721,\cdot)\) \(\chi_{4830}(4351,\cdot)\) \(\chi_{4830}(4741,\cdot)\)

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: 33.33.277966181338944111003326058293667039541136678070715028736001.1

Values on generators

\((3221,967,2761,1891)\) → \((1,1,e\left(\frac{1}{3}\right),e\left(\frac{9}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{2}{3}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(121,a) \;\) at \(\;a = \) e.g. 2