Properties

Label 6025.604
Modulus $6025$
Conductor $6025$
Order $30$
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([3,29]))
 
pari: [g,chi] = znchar(Mod(604,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
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.dz

\(\chi_{6025}(604,\cdot)\) \(\chi_{6025}(864,\cdot)\) \(\chi_{6025}(1834,\cdot)\) \(\chi_{6025}(1904,\cdot)\) \(\chi_{6025}(2709,\cdot)\) \(\chi_{6025}(4419,\cdot)\) \(\chi_{6025}(5489,\cdot)\) \(\chi_{6025}(5794,\cdot)\)

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

\((2652,2176)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{29}{30}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{3}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial