Properties

Label 3920.53
Modulus $3920$
Conductor $3920$
Order $84$
Real no
Primitive yes
Minimal yes
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([0,21,63,20]))
 
pari: [g,chi] = znchar(Mod(53,3920))
 

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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.ga

\(\chi_{3920}(53,\cdot)\) \(\chi_{3920}(317,\cdot)\) \(\chi_{3920}(613,\cdot)\) \(\chi_{3920}(877,\cdot)\) \(\chi_{3920}(933,\cdot)\) \(\chi_{3920}(1117,\cdot)\) \(\chi_{3920}(1173,\cdot)\) \(\chi_{3920}(1437,\cdot)\) \(\chi_{3920}(1493,\cdot)\) \(\chi_{3920}(1677,\cdot)\) \(\chi_{3920}(1997,\cdot)\) \(\chi_{3920}(2053,\cdot)\) \(\chi_{3920}(2237,\cdot)\) \(\chi_{3920}(2293,\cdot)\) \(\chi_{3920}(2557,\cdot)\) \(\chi_{3920}(2613,\cdot)\) \(\chi_{3920}(2797,\cdot)\) \(\chi_{3920}(2853,\cdot)\) \(\chi_{3920}(3173,\cdot)\) \(\chi_{3920}(3357,\cdot)\) \(\chi_{3920}(3413,\cdot)\) \(\chi_{3920}(3677,\cdot)\) \(\chi_{3920}(3733,\cdot)\) \(\chi_{3920}(3917,\cdot)\)

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

\((1471,981,3137,3041)\) → \((1,i,-i,e\left(\frac{5}{21}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{59}{84}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{67}{84}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{15}{28}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2