Properties

Label 3920.109
Modulus $3920$
Conductor $3920$
Order $84$
Real no
Primitive yes
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([0,63,42,80]))
 
pari: [g,chi] = znchar(Mod(109,3920))
 

Basic properties

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

Galois orbit 3920.fq

\(\chi_{3920}(109,\cdot)\) \(\chi_{3920}(149,\cdot)\) \(\chi_{3920}(389,\cdot)\) \(\chi_{3920}(429,\cdot)\) \(\chi_{3920}(669,\cdot)\) \(\chi_{3920}(709,\cdot)\) \(\chi_{3920}(989,\cdot)\) \(\chi_{3920}(1229,\cdot)\) \(\chi_{3920}(1269,\cdot)\) \(\chi_{3920}(1509,\cdot)\) \(\chi_{3920}(1789,\cdot)\) \(\chi_{3920}(1829,\cdot)\) \(\chi_{3920}(2069,\cdot)\) \(\chi_{3920}(2109,\cdot)\) \(\chi_{3920}(2349,\cdot)\) \(\chi_{3920}(2389,\cdot)\) \(\chi_{3920}(2629,\cdot)\) \(\chi_{3920}(2669,\cdot)\) \(\chi_{3920}(2949,\cdot)\) \(\chi_{3920}(3189,\cdot)\) \(\chi_{3920}(3229,\cdot)\) \(\chi_{3920}(3469,\cdot)\) \(\chi_{3920}(3749,\cdot)\) \(\chi_{3920}(3789,\cdot)\)

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

\((1471,981,3137,3041)\) → \((1,-i,-1,e\left(\frac{20}{21}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{59}{84}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{71}{84}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{11}{28}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2