Properties

Label 3920.2367
Modulus $3920$
Conductor $980$
Order $28$
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(28))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,0,7,20]))
 
pari: [g,chi] = znchar(Mod(2367,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(980\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(28\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{980}(407,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.em

\(\chi_{3920}(127,\cdot)\) \(\chi_{3920}(463,\cdot)\) \(\chi_{3920}(1023,\cdot)\) \(\chi_{3920}(1247,\cdot)\) \(\chi_{3920}(1583,\cdot)\) \(\chi_{3920}(1807,\cdot)\) \(\chi_{3920}(2143,\cdot)\) \(\chi_{3920}(2367,\cdot)\) \(\chi_{3920}(2703,\cdot)\) \(\chi_{3920}(2927,\cdot)\) \(\chi_{3920}(3263,\cdot)\) \(\chi_{3920}(3487,\cdot)\)

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: 28.28.4698031131813648056477467012100308504166528000000000000000000000.1

Values on generators

\((1471,981,3137,3041)\) → \((-1,1,i,e\left(\frac{5}{7}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{3}{28}\right)\)\(1\)\(e\left(\frac{11}{28}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{5}{14}\right)\)\(-1\)
value at e.g. 2