Properties

Label 2960.823
Modulus $2960$
Conductor $1480$
Order $36$
Real no
Primitive no
Minimal no
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([18,18,27,16]))
 
pari: [g,chi] = znchar(Mod(823,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(1480\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1480}(83,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.gi

\(\chi_{2960}(7,\cdot)\) \(\chi_{2960}(423,\cdot)\) \(\chi_{2960}(567,\cdot)\) \(\chi_{2960}(663,\cdot)\) \(\chi_{2960}(823,\cdot)\) \(\chi_{2960}(1143,\cdot)\) \(\chi_{2960}(1607,\cdot)\) \(\chi_{2960}(1783,\cdot)\) \(\chi_{2960}(1847,\cdot)\) \(\chi_{2960}(2007,\cdot)\) \(\chi_{2960}(2327,\cdot)\) \(\chi_{2960}(2343,\cdot)\)

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: Number field defined by a degree 36 polynomial

Values on generators

\((2591,741,1777,2481)\) → \((-1,-1,-i,e\left(\frac{4}{9}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(823, a) \) \(1\)\(1\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{5}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(823,a) \;\) at \(\;a = \) e.g. 2