Properties

Label 6025.331
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([24,53]))
 
pari: [g,chi] = znchar(Mod(331,6025))
 

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.fp

\(\chi_{6025}(331,\cdot)\) \(\chi_{6025}(616,\cdot)\) \(\chi_{6025}(641,\cdot)\) \(\chi_{6025}(846,\cdot)\) \(\chi_{6025}(1061,\cdot)\) \(\chi_{6025}(1356,\cdot)\) \(\chi_{6025}(2046,\cdot)\) \(\chi_{6025}(2506,\cdot)\) \(\chi_{6025}(3036,\cdot)\) \(\chi_{6025}(4421,\cdot)\) \(\chi_{6025}(4496,\cdot)\) \(\chi_{6025}(4811,\cdot)\) \(\chi_{6025}(5206,\cdot)\) \(\chi_{6025}(5311,\cdot)\) \(\chi_{6025}(5866,\cdot)\) \(\chi_{6025}(5891,\cdot)\)

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

\((2652,2176)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{53}{60}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{7}{60}\right)\)
value at e.g. 2

Related number fields

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