Properties

Label 4560.3353
Modulus $4560$
Conductor $2280$
Order $36$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4560, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,18,18,27,16]))
 
pari: [g,chi] = znchar(Mod(3353,4560))
 

Basic properties

Modulus: \(4560\)
Conductor: \(2280\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2280}(2213,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4560.hu

\(\chi_{4560}(137,\cdot)\) \(\chi_{4560}(233,\cdot)\) \(\chi_{4560}(377,\cdot)\) \(\chi_{4560}(473,\cdot)\) \(\chi_{4560}(617,\cdot)\) \(\chi_{4560}(2057,\cdot)\) \(\chi_{4560}(2153,\cdot)\) \(\chi_{4560}(2297,\cdot)\) \(\chi_{4560}(2873,\cdot)\) \(\chi_{4560}(3113,\cdot)\) \(\chi_{4560}(3353,\cdot)\) \(\chi_{4560}(3977,\cdot)\)

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

\((1711,1141,3041,2737,1921)\) → \((1,-1,-1,-i,e\left(\frac{4}{9}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{35}{36}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{2}{3}\right)\)\(i\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{31}{36}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4560 }(3353,a) \;\) at \(\;a = \) e.g. 2