Properties

Label 6025.9
Modulus $6025$
Conductor $6025$
Order $60$
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([42,31]))
 
pari: [g,chi] = znchar(Mod(9,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
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.gt

\(\chi_{6025}(9,\cdot)\) \(\chi_{6025}(564,\cdot)\) \(\chi_{6025}(589,\cdot)\) \(\chi_{6025}(1054,\cdot)\) \(\chi_{6025}(1339,\cdot)\) \(\chi_{6025}(1364,\cdot)\) \(\chi_{6025}(1569,\cdot)\) \(\chi_{6025}(1784,\cdot)\) \(\chi_{6025}(2079,\cdot)\) \(\chi_{6025}(2769,\cdot)\) \(\chi_{6025}(3229,\cdot)\) \(\chi_{6025}(3759,\cdot)\) \(\chi_{6025}(5144,\cdot)\) \(\chi_{6025}(5219,\cdot)\) \(\chi_{6025}(5534,\cdot)\) \(\chi_{6025}(5929,\cdot)\)

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

\((2652,2176)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{31}{60}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial