Properties

Label 6001.766
Modulus $6001$
Conductor $353$
Order $16$
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(6001)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,13]))
 
pari: [g,chi] = znchar(Mod(766,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(353\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{353}(60,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.bc

\(\chi_{6001}(766,\cdot)\) \(\chi_{6001}(2058,\cdot)\) \(\chi_{6001}(4200,\cdot)\) \(\chi_{6001}(4285,\cdot)\) \(\chi_{6001}(4336,\cdot)\) \(\chi_{6001}(4489,\cdot)\) \(\chi_{6001}(4540,\cdot)\) \(\chi_{6001}(4625,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((2825,3180)\) → \((1,e\left(\frac{13}{16}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(i\)\(e\left(\frac{13}{16}\right)\)\(-1\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(-i\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{16}\right)\)\(-i\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{16})\)
Fixed field: 16.16.164672311157017194379126294334593898657.1