Properties

Label 6025.214
Modulus $6025$
Conductor $6025$
Order $40$
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([12,31]))
 
pari: [g,chi] = znchar(Mod(214,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
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.fa

\(\chi_{6025}(214,\cdot)\) \(\chi_{6025}(644,\cdot)\) \(\chi_{6025}(764,\cdot)\) \(\chi_{6025}(969,\cdot)\) \(\chi_{6025}(1164,\cdot)\) \(\chi_{6025}(1714,\cdot)\) \(\chi_{6025}(1734,\cdot)\) \(\chi_{6025}(3369,\cdot)\) \(\chi_{6025}(3554,\cdot)\) \(\chi_{6025}(3694,\cdot)\) \(\chi_{6025}(3809,\cdot)\) \(\chi_{6025}(3904,\cdot)\) \(\chi_{6025}(5254,\cdot)\) \(\chi_{6025}(5604,\cdot)\) \(\chi_{6025}(5659,\cdot)\) \(\chi_{6025}(5909,\cdot)\)

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

\((2652,2176)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{31}{40}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{7}{40}\right)\)\(i\)\(e\left(\frac{1}{8}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: Number field defined by a degree 40 polynomial