Properties

Label 3920.87
Modulus $3920$
Conductor $1960$
Order $84$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

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([42,42,21,38]))
 
pari: [g,chi] = znchar(Mod(87,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(1960\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1960}(1067,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.fw

\(\chi_{3920}(87,\cdot)\) \(\chi_{3920}(103,\cdot)\) \(\chi_{3920}(327,\cdot)\) \(\chi_{3920}(647,\cdot)\) \(\chi_{3920}(663,\cdot)\) \(\chi_{3920}(887,\cdot)\) \(\chi_{3920}(983,\cdot)\) \(\chi_{3920}(1223,\cdot)\) \(\chi_{3920}(1447,\cdot)\) \(\chi_{3920}(1543,\cdot)\) \(\chi_{3920}(1767,\cdot)\) \(\chi_{3920}(2007,\cdot)\) \(\chi_{3920}(2103,\cdot)\) \(\chi_{3920}(2327,\cdot)\) \(\chi_{3920}(2343,\cdot)\) \(\chi_{3920}(2663,\cdot)\) \(\chi_{3920}(2887,\cdot)\) \(\chi_{3920}(2903,\cdot)\) \(\chi_{3920}(3127,\cdot)\) \(\chi_{3920}(3223,\cdot)\) \(\chi_{3920}(3447,\cdot)\) \(\chi_{3920}(3463,\cdot)\) \(\chi_{3920}(3687,\cdot)\) \(\chi_{3920}(3783,\cdot)\)

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

\((1471,981,3137,3041)\) → \((-1,-1,i,e\left(\frac{19}{42}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{47}{84}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{37}{84}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2