Properties

Label 6025.493
Modulus $6025$
Conductor $1205$
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(6025)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([36,5]))
 
pari: [g,chi] = znchar(Mod(493,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(493,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.fn

\(\chi_{6025}(493,\cdot)\) \(\chi_{6025}(1268,\cdot)\) \(\chi_{6025}(1357,\cdot)\) \(\chi_{6025}(1668,\cdot)\) \(\chi_{6025}(1993,\cdot)\) \(\chi_{6025}(2207,\cdot)\) \(\chi_{6025}(2257,\cdot)\) \(\chi_{6025}(2432,\cdot)\) \(\chi_{6025}(3068,\cdot)\) \(\chi_{6025}(3393,\cdot)\) \(\chi_{6025}(3793,\cdot)\) \(\chi_{6025}(4557,\cdot)\) \(\chi_{6025}(4568,\cdot)\) \(\chi_{6025}(4732,\cdot)\) \(\chi_{6025}(4782,\cdot)\) \(\chi_{6025}(5632,\cdot)\)

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

\((2652,2176)\) → \((-i,e\left(\frac{5}{48}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{1}{12}\right)\)\(-i\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{7}{48}\right)\)
value at e.g. 2

Related number fields

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