Properties

Label 2960.1857
Modulus $2960$
Conductor $185$
Order $36$
Real no
Primitive no
Minimal no
Parity odd

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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([0,0,9,32]))
 
pari: [g,chi] = znchar(Mod(1857,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(185\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{185}(7,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.gk

\(\chi_{2960}(33,\cdot)\) \(\chi_{2960}(497,\cdot)\) \(\chi_{2960}(673,\cdot)\) \(\chi_{2960}(737,\cdot)\) \(\chi_{2960}(897,\cdot)\) \(\chi_{2960}(1217,\cdot)\) \(\chi_{2960}(1233,\cdot)\) \(\chi_{2960}(1857,\cdot)\) \(\chi_{2960}(2273,\cdot)\) \(\chi_{2960}(2417,\cdot)\) \(\chi_{2960}(2513,\cdot)\) \(\chi_{2960}(2673,\cdot)\)

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: 36.0.1134084166835624937413663701523229292665702790961273014545440673828125.1

Values on generators

\((2591,741,1777,2481)\) → \((1,1,i,e\left(\frac{8}{9}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(1857, a) \) \(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(1857,a) \;\) at \(\;a = \) e.g. 2