Properties

Label 2960.261
Modulus $2960$
Conductor $592$
Order $36$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

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([0,9,0,1]))
 
pari: [g,chi] = znchar(Mod(261,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(592\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{592}(261,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.he

\(\chi_{2960}(261,\cdot)\) \(\chi_{2960}(301,\cdot)\) \(\chi_{2960}(461,\cdot)\) \(\chi_{2960}(501,\cdot)\) \(\chi_{2960}(661,\cdot)\) \(\chi_{2960}(701,\cdot)\) \(\chi_{2960}(1021,\cdot)\) \(\chi_{2960}(1461,\cdot)\) \(\chi_{2960}(1541,\cdot)\) \(\chi_{2960}(2381,\cdot)\) \(\chi_{2960}(2461,\cdot)\) \(\chi_{2960}(2901,\cdot)\)

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: 36.0.4886860176107258124616704873602845327686728999915307588219200292503475176863258640384.1

Values on generators

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

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(-1\)\(1\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{7}{36}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(261,a) \;\) at \(\;a = \) e.g. 2