Properties

Label 2601.65
Modulus $2601$
Conductor $153$
Order $48$
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(2601, base_ring=CyclotomicField(48))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([8,27]))
 
pari: [g,chi] = znchar(Mod(65,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(153\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{153}(65,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.w

\(\chi_{2601}(65,\cdot)\) \(\chi_{2601}(131,\cdot)\) \(\chi_{2601}(158,\cdot)\) \(\chi_{2601}(329,\cdot)\) \(\chi_{2601}(653,\cdot)\) \(\chi_{2601}(932,\cdot)\) \(\chi_{2601}(1091,\cdot)\) \(\chi_{2601}(1370,\cdot)\) \(\chi_{2601}(1694,\cdot)\) \(\chi_{2601}(1865,\cdot)\) \(\chi_{2601}(1892,\cdot)\) \(\chi_{2601}(1958,\cdot)\) \(\chi_{2601}(2063,\cdot)\) \(\chi_{2601}(2237,\cdot)\) \(\chi_{2601}(2387,\cdot)\) \(\chi_{2601}(2561,\cdot)\)

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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

\((290,2026)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{9}{16}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{31}{48}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2