Properties

Label 3920.267
Modulus $3920$
Conductor $3920$
Order $28$
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(28))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,7,7,16]))
 
pari: [g,chi] = znchar(Mod(267,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(3920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(28\)
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.dv

\(\chi_{3920}(267,\cdot)\) \(\chi_{3920}(323,\cdot)\) \(\chi_{3920}(827,\cdot)\) \(\chi_{3920}(1387,\cdot)\) \(\chi_{3920}(1443,\cdot)\) \(\chi_{3920}(1947,\cdot)\) \(\chi_{3920}(2003,\cdot)\) \(\chi_{3920}(2507,\cdot)\) \(\chi_{3920}(2563,\cdot)\) \(\chi_{3920}(3067,\cdot)\) \(\chi_{3920}(3123,\cdot)\) \(\chi_{3920}(3683,\cdot)\)

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: \(\Q(\zeta_{28})\)
Fixed field: 28.28.2644756406826366870359203089991553685508052418280592244736000000000000000000000.2

Values on generators

\((1471,981,3137,3041)\) → \((-1,i,i,e\left(\frac{4}{7}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{15}{28}\right)\)\(-i\)\(e\left(\frac{13}{28}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{15}{28}\right)\)\(-1\)
value at e.g. 2