Properties

Label 6025.272
Modulus $6025$
Conductor $6025$
Order $240$
Real no
Primitive yes
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([204,151]))
 
pari: [g,chi] = znchar(Mod(272,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.ja

\(\chi_{6025}(272,\cdot)\) \(\chi_{6025}(287,\cdot)\) \(\chi_{6025}(297,\cdot)\) \(\chi_{6025}(303,\cdot)\) \(\chi_{6025}(353,\cdot)\) \(\chi_{6025}(383,\cdot)\) \(\chi_{6025}(427,\cdot)\) \(\chi_{6025}(517,\cdot)\) \(\chi_{6025}(577,\cdot)\) \(\chi_{6025}(792,\cdot)\) \(\chi_{6025}(912,\cdot)\) \(\chi_{6025}(1042,\cdot)\) \(\chi_{6025}(1113,\cdot)\) \(\chi_{6025}(1337,\cdot)\) \(\chi_{6025}(1453,\cdot)\) \(\chi_{6025}(1517,\cdot)\) \(\chi_{6025}(1538,\cdot)\) \(\chi_{6025}(1653,\cdot)\) \(\chi_{6025}(1858,\cdot)\) \(\chi_{6025}(1872,\cdot)\) \(\chi_{6025}(1897,\cdot)\) \(\chi_{6025}(2002,\cdot)\) \(\chi_{6025}(2037,\cdot)\) \(\chi_{6025}(2083,\cdot)\) \(\chi_{6025}(2203,\cdot)\) \(\chi_{6025}(2208,\cdot)\) \(\chi_{6025}(2373,\cdot)\) \(\chi_{6025}(2403,\cdot)\) \(\chi_{6025}(2462,\cdot)\) \(\chi_{6025}(2577,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{151}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{47}{120}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{211}{240}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{79}{240}\right)\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{173}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial