Properties

Label 4235.1594
Modulus $4235$
Conductor $4235$
Order $66$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4235, base_ring=CyclotomicField(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,55,57]))
 
pari: [g,chi] = znchar(Mod(1594,4235))
 

Basic properties

Modulus: \(4235\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4235.co

\(\chi_{4235}(54,\cdot)\) \(\chi_{4235}(164,\cdot)\) \(\chi_{4235}(439,\cdot)\) \(\chi_{4235}(549,\cdot)\) \(\chi_{4235}(824,\cdot)\) \(\chi_{4235}(934,\cdot)\) \(\chi_{4235}(1319,\cdot)\) \(\chi_{4235}(1594,\cdot)\) \(\chi_{4235}(1704,\cdot)\) \(\chi_{4235}(1979,\cdot)\) \(\chi_{4235}(2089,\cdot)\) \(\chi_{4235}(2364,\cdot)\) \(\chi_{4235}(2474,\cdot)\) \(\chi_{4235}(2749,\cdot)\) \(\chi_{4235}(2859,\cdot)\) \(\chi_{4235}(3134,\cdot)\) \(\chi_{4235}(3244,\cdot)\) \(\chi_{4235}(3519,\cdot)\) \(\chi_{4235}(3904,\cdot)\) \(\chi_{4235}(4014,\cdot)\)

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

\((2542,1816,2906)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{19}{22}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(12\)\(13\)\(16\)\(17\)
\(1\)\(1\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{43}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4235 }(1594,a) \;\) at \(\;a = \) e.g. 2