Properties

Label 4235.1119
Modulus $4235$
Conductor $4235$
Order $110$
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(110))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([55,55,53]))
 
pari: [g,chi] = znchar(Mod(1119,4235))
 

Basic properties

Modulus: \(4235\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(110\)
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.cv

\(\chi_{4235}(139,\cdot)\) \(\chi_{4235}(244,\cdot)\) \(\chi_{4235}(314,\cdot)\) \(\chi_{4235}(349,\cdot)\) \(\chi_{4235}(629,\cdot)\) \(\chi_{4235}(734,\cdot)\) \(\chi_{4235}(909,\cdot)\) \(\chi_{4235}(1014,\cdot)\) \(\chi_{4235}(1084,\cdot)\) \(\chi_{4235}(1119,\cdot)\) \(\chi_{4235}(1294,\cdot)\) \(\chi_{4235}(1399,\cdot)\) \(\chi_{4235}(1469,\cdot)\) \(\chi_{4235}(1504,\cdot)\) \(\chi_{4235}(1679,\cdot)\) \(\chi_{4235}(1784,\cdot)\) \(\chi_{4235}(1854,\cdot)\) \(\chi_{4235}(1889,\cdot)\) \(\chi_{4235}(2064,\cdot)\) \(\chi_{4235}(2239,\cdot)\) \(\chi_{4235}(2274,\cdot)\) \(\chi_{4235}(2449,\cdot)\) \(\chi_{4235}(2554,\cdot)\) \(\chi_{4235}(2624,\cdot)\) \(\chi_{4235}(2834,\cdot)\) \(\chi_{4235}(2939,\cdot)\) \(\chi_{4235}(3009,\cdot)\) \(\chi_{4235}(3044,\cdot)\) \(\chi_{4235}(3219,\cdot)\) \(\chi_{4235}(3324,\cdot)\) ...

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: $\Q(\zeta_{55})$
Fixed field: Number field defined by a degree 110 polynomial (not computed)

Values on generators

\((2542,1816,2906)\) → \((-1,-1,e\left(\frac{53}{110}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(12\)\(13\)\(16\)\(17\)
\(1\)\(1\)\(e\left(\frac{54}{55}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{53}{55}\right)\)\(e\left(\frac{21}{55}\right)\)\(e\left(\frac{52}{55}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{73}{110}\right)\)\(e\left(\frac{51}{55}\right)\)\(e\left(\frac{67}{110}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4235 }(1119,a) \;\) at \(\;a = \) e.g. 2