Properties

Label 2960.1919
Modulus $2960$
Conductor $740$
Order $36$
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(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,0,18,5]))
 
pari: [g,chi] = znchar(Mod(1919,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(740\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{740}(439,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.gm

\(\chi_{2960}(79,\cdot)\) \(\chi_{2960}(239,\cdot)\) \(\chi_{2960}(479,\cdot)\) \(\chi_{2960}(799,\cdot)\) \(\chi_{2960}(1199,\cdot)\) \(\chi_{2960}(1519,\cdot)\) \(\chi_{2960}(1759,\cdot)\) \(\chi_{2960}(1919,\cdot)\) \(\chi_{2960}(2159,\cdot)\) \(\chi_{2960}(2239,\cdot)\) \(\chi_{2960}(2719,\cdot)\) \(\chi_{2960}(2799,\cdot)\)

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: \(\Q(\zeta_{36})\)
Fixed field: 36.36.2021157996966699236888348986167488408933250634681517576814592000000000000000000.1

Values on generators

\((2591,741,1777,2481)\) → \((-1,1,-1,e\left(\frac{5}{36}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(1919, a) \) \(1\)\(1\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{13}{36}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{5}{6}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(1919,a) \;\) at \(\;a = \) e.g. 2