Properties

Label 6025.13
Modulus $6025$
Conductor $6025$
Order $240$
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([228,47]))
 
pari: [g,chi] = znchar(Mod(13,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.jb

\(\chi_{6025}(13,\cdot)\) \(\chi_{6025}(137,\cdot)\) \(\chi_{6025}(142,\cdot)\) \(\chi_{6025}(398,\cdot)\) \(\chi_{6025}(758,\cdot)\) \(\chi_{6025}(837,\cdot)\) \(\chi_{6025}(927,\cdot)\) \(\chi_{6025}(978,\cdot)\) \(\chi_{6025}(1033,\cdot)\) \(\chi_{6025}(1048,\cdot)\) \(\chi_{6025}(1283,\cdot)\) \(\chi_{6025}(1378,\cdot)\) \(\chi_{6025}(1512,\cdot)\) \(\chi_{6025}(1577,\cdot)\) \(\chi_{6025}(1617,\cdot)\) \(\chi_{6025}(1758,\cdot)\) \(\chi_{6025}(1842,\cdot)\) \(\chi_{6025}(1862,\cdot)\) \(\chi_{6025}(1873,\cdot)\) \(\chi_{6025}(1877,\cdot)\) \(\chi_{6025}(1967,\cdot)\) \(\chi_{6025}(2023,\cdot)\) \(\chi_{6025}(2127,\cdot)\) \(\chi_{6025}(2452,\cdot)\) \(\chi_{6025}(2472,\cdot)\) \(\chi_{6025}(2478,\cdot)\) \(\chi_{6025}(2522,\cdot)\) \(\chi_{6025}(2537,\cdot)\) \(\chi_{6025}(2638,\cdot)\) \(\chi_{6025}(2702,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{47}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{19}{120}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{227}{240}\right)\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{23}{240}\right)\)\(e\left(\frac{73}{120}\right)\)\(e\left(\frac{61}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial