Properties

Label 4830.83
Modulus $4830$
Conductor $2415$
Order $44$
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(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,33,22,42]))
 
pari: [g,chi] = znchar(Mod(83,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(2415\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2415}(83,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.cp

\(\chi_{4830}(83,\cdot)\) \(\chi_{4830}(293,\cdot)\) \(\chi_{4830}(503,\cdot)\) \(\chi_{4830}(797,\cdot)\) \(\chi_{4830}(1217,\cdot)\) \(\chi_{4830}(1763,\cdot)\) \(\chi_{4830}(1847,\cdot)\) \(\chi_{4830}(2057,\cdot)\) \(\chi_{4830}(2183,\cdot)\) \(\chi_{4830}(2687,\cdot)\) \(\chi_{4830}(2813,\cdot)\) \(\chi_{4830}(3023,\cdot)\) \(\chi_{4830}(3317,\cdot)\) \(\chi_{4830}(3653,\cdot)\) \(\chi_{4830}(3737,\cdot)\) \(\chi_{4830}(3947,\cdot)\) \(\chi_{4830}(4157,\cdot)\) \(\chi_{4830}(4283,\cdot)\) \(\chi_{4830}(4367,\cdot)\) \(\chi_{4830}(4703,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Values on generators

\((3221,967,2761,1891)\) → \((-1,-i,-1,e\left(\frac{21}{22}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(-i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(83,a) \;\) at \(\;a = \) e.g. 2