Properties

Label 6025.651
Modulus $6025$
Conductor $241$
Order $120$
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([0,47]))
 
pari: [g,chi] = znchar(Mod(651,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(241\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{241}(169,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.in

\(\chi_{6025}(651,\cdot)\) \(\chi_{6025}(726,\cdot)\) \(\chi_{6025}(776,\cdot)\) \(\chi_{6025}(976,\cdot)\) \(\chi_{6025}(1176,\cdot)\) \(\chi_{6025}(1401,\cdot)\) \(\chi_{6025}(1426,\cdot)\) \(\chi_{6025}(1526,\cdot)\) \(\chi_{6025}(1851,\cdot)\) \(\chi_{6025}(2151,\cdot)\) \(\chi_{6025}(2351,\cdot)\) \(\chi_{6025}(2576,\cdot)\) \(\chi_{6025}(2601,\cdot)\) \(\chi_{6025}(2701,\cdot)\) \(\chi_{6025}(2726,\cdot)\) \(\chi_{6025}(2951,\cdot)\) \(\chi_{6025}(3151,\cdot)\) \(\chi_{6025}(3451,\cdot)\) \(\chi_{6025}(3776,\cdot)\) \(\chi_{6025}(3876,\cdot)\) \(\chi_{6025}(3901,\cdot)\) \(\chi_{6025}(4126,\cdot)\) \(\chi_{6025}(4326,\cdot)\) \(\chi_{6025}(4526,\cdot)\) \(\chi_{6025}(4576,\cdot)\) \(\chi_{6025}(4651,\cdot)\) \(\chi_{6025}(5351,\cdot)\) \(\chi_{6025}(5476,\cdot)\) \(\chi_{6025}(5651,\cdot)\) \(\chi_{6025}(5676,\cdot)\) ...

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

\((2652,2176)\) → \((1,e\left(\frac{47}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{47}{120}\right)\)\(i\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{49}{120}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial