Properties

Label 3920.71
Modulus $3920$
Conductor $392$
Order $14$
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(14))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([7,7,0,8]))
 
pari: [g,chi] = znchar(Mod(71,3920))
 

Basic properties

Modulus: \(3920\)
Conductor: \(392\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(14\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{392}(267,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3920.df

\(\chi_{3920}(71,\cdot)\) \(\chi_{3920}(631,\cdot)\) \(\chi_{3920}(1191,\cdot)\) \(\chi_{3920}(1751,\cdot)\) \(\chi_{3920}(2311,\cdot)\) \(\chi_{3920}(2871,\cdot)\)

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: \(\Q(\zeta_{7})\)
Fixed field: 14.0.401774962552217617093885952.1

Values on generators

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

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{2}{7}\right)\)\(1\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{11}{14}\right)\)\(-1\)
value at e.g. 2