Properties

Label 2960.1451
Modulus $2960$
Conductor $592$
Order $12$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2960, base_ring=CyclotomicField(12))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6,3,0,1]))
 
pari: [g,chi] = znchar(Mod(1451,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(592\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{592}(267,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.dx

\(\chi_{2960}(51,\cdot)\) \(\chi_{2960}(171,\cdot)\) \(\chi_{2960}(1451,\cdot)\) \(\chi_{2960}(1731,\cdot)\)

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: \(\Q(\zeta_{12})\)
Fixed field: 12.12.1528300733849759596723306496.2

Values on generators

\((2591,741,1777,2481)\) → \((-1,i,1,e\left(\frac{1}{12}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(1451, a) \) \(1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(i\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{12}\right)\)\(i\)\(i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(1451,a) \;\) at \(\;a = \) e.g. 2