Properties

Label 2601.688
Modulus $2601$
Conductor $153$
Order $24$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2601, base_ring=CyclotomicField(24))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([8,15]))
 
pari: [g,chi] = znchar(Mod(688,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(153\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{153}(76,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.s

\(\chi_{2601}(688,\cdot)\) \(\chi_{2601}(733,\cdot)\) \(\chi_{2601}(1555,\cdot)\) \(\chi_{2601}(1579,\cdot)\) \(\chi_{2601}(1600,\cdot)\) \(\chi_{2601}(1624,\cdot)\) \(\chi_{2601}(2446,\cdot)\) \(\chi_{2601}(2491,\cdot)\)

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: \(\Q(\zeta_{24})\)
Fixed field: 24.24.128028748427622359924863503266793533356497.1

Values on generators

\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{8}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(i\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{1}{3}\right)\)
value at e.g. 2