Properties

Label 1600.43
Modulus $1600$
Conductor $320$
Order $16$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1600, base_ring=CyclotomicField(16))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([8,13,12]))
 
pari: [g,chi] = znchar(Mod(43,1600))
 

Basic properties

Modulus: \(1600\)
Conductor: \(320\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{320}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1600.bl

\(\chi_{1600}(43,\cdot)\) \(\chi_{1600}(307,\cdot)\) \(\chi_{1600}(443,\cdot)\) \(\chi_{1600}(707,\cdot)\) \(\chi_{1600}(843,\cdot)\) \(\chi_{1600}(1107,\cdot)\) \(\chi_{1600}(1243,\cdot)\) \(\chi_{1600}(1507,\cdot)\)

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: \(\Q(\zeta_{16})\)
Fixed field: 16.16.147573952589676412928000000000000.1

Values on generators

\((1151,901,577)\) → \((-1,e\left(\frac{13}{16}\right),-i)\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(1\)\(1\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(-1\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{9}{16}\right)\)
value at e.g. 2