Properties

Label 3920.131
Modulus $3920$
Conductor $784$
Order $84$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3920, base_ring=CyclotomicField(84))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([42,63,0,82]))
 
pari: [g,chi] = znchar(Mod(131,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(784\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{784}(131,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.fr

\(\chi_{3920}(131,\cdot)\) \(\chi_{3920}(171,\cdot)\) \(\chi_{3920}(451,\cdot)\) \(\chi_{3920}(691,\cdot)\) \(\chi_{3920}(731,\cdot)\) \(\chi_{3920}(971,\cdot)\) \(\chi_{3920}(1251,\cdot)\) \(\chi_{3920}(1291,\cdot)\) \(\chi_{3920}(1531,\cdot)\) \(\chi_{3920}(1571,\cdot)\) \(\chi_{3920}(1811,\cdot)\) \(\chi_{3920}(1851,\cdot)\) \(\chi_{3920}(2091,\cdot)\) \(\chi_{3920}(2131,\cdot)\) \(\chi_{3920}(2411,\cdot)\) \(\chi_{3920}(2651,\cdot)\) \(\chi_{3920}(2691,\cdot)\) \(\chi_{3920}(2931,\cdot)\) \(\chi_{3920}(3211,\cdot)\) \(\chi_{3920}(3251,\cdot)\) \(\chi_{3920}(3491,\cdot)\) \(\chi_{3920}(3531,\cdot)\) \(\chi_{3920}(3771,\cdot)\) \(\chi_{3920}(3811,\cdot)\)

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: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial

Values on generators

\((1471,981,3137,3041)\) → \((-1,-i,1,e\left(\frac{41}{42}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{61}{84}\right)\)\(e\left(\frac{19}{42}\right)\)\(e\left(\frac{25}{84}\right)\)\(e\left(\frac{13}{28}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{23}{28}\right)\)\(e\left(\frac{1}{3}\right)\)
value at e.g. 2