Properties

Label 4830.149
Modulus $4830$
Conductor $2415$
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([33,33,22,27]))
 
pari: [g,chi] = znchar(Mod(149,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(2415\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2415}(149,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.dh

\(\chi_{4830}(149,\cdot)\) \(\chi_{4830}(359,\cdot)\) \(\chi_{4830}(389,\cdot)\) \(\chi_{4830}(569,\cdot)\) \(\chi_{4830}(779,\cdot)\) \(\chi_{4830}(1019,\cdot)\) \(\chi_{4830}(1229,\cdot)\) \(\chi_{4830}(1859,\cdot)\) \(\chi_{4830}(2039,\cdot)\) \(\chi_{4830}(2459,\cdot)\) \(\chi_{4830}(2489,\cdot)\) \(\chi_{4830}(2909,\cdot)\) \(\chi_{4830}(3089,\cdot)\) \(\chi_{4830}(3119,\cdot)\) \(\chi_{4830}(3299,\cdot)\) \(\chi_{4830}(3329,\cdot)\) \(\chi_{4830}(3539,\cdot)\) \(\chi_{4830}(3929,\cdot)\) \(\chi_{4830}(4559,\cdot)\) \(\chi_{4830}(4799,\cdot)\)

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

\((3221,967,2761,1891)\) → \((-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{9}{22}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{13}{66}\right)\)\(e\left(\frac{53}{66}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{26}{33}\right)\)\(e\left(\frac{25}{33}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{2}{3}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(149,a) \;\) at \(\;a = \) e.g. 2