Properties

Label 6025.324
Modulus $6025$
Conductor $1205$
Order $60$
Real no
Primitive no
Minimal no
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([30,37]))
 
pari: [g,chi] = znchar(Mod(324,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(324,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.fo

\(\chi_{6025}(324,\cdot)\) \(\chi_{6025}(399,\cdot)\) \(\chi_{6025}(874,\cdot)\) \(\chi_{6025}(1349,\cdot)\) \(\chi_{6025}(2024,\cdot)\) \(\chi_{6025}(2774,\cdot)\) \(\chi_{6025}(2974,\cdot)\) \(\chi_{6025}(2999,\cdot)\) \(\chi_{6025}(3124,\cdot)\) \(\chi_{6025}(3624,\cdot)\) \(\chi_{6025}(3749,\cdot)\) \(\chi_{6025}(3774,\cdot)\) \(\chi_{6025}(3974,\cdot)\) \(\chi_{6025}(4724,\cdot)\) \(\chi_{6025}(5399,\cdot)\) \(\chi_{6025}(5874,\cdot)\)

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

\((2652,2176)\) → \((-1,e\left(\frac{37}{60}\right))\)

Values

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

Related number fields

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