Properties

Label 3920.57
Modulus $3920$
Conductor $1960$
Order $28$
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(28))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,14,7,24]))
 
pari: [g,chi] = znchar(Mod(57,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(1960\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(28\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1960}(1037,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.el

\(\chi_{3920}(57,\cdot)\) \(\chi_{3920}(617,\cdot)\) \(\chi_{3920}(953,\cdot)\) \(\chi_{3920}(1513,\cdot)\) \(\chi_{3920}(1737,\cdot)\) \(\chi_{3920}(2073,\cdot)\) \(\chi_{3920}(2297,\cdot)\) \(\chi_{3920}(2633,\cdot)\) \(\chi_{3920}(2857,\cdot)\) \(\chi_{3920}(3193,\cdot)\) \(\chi_{3920}(3417,\cdot)\) \(\chi_{3920}(3753,\cdot)\)

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: 28.0.76972542063634809757326819526251454532264394752000000000000000000000.1

Values on generators

\((1471,981,3137,3041)\) → \((1,-1,i,e\left(\frac{6}{7}\right))\)

Values

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