Properties

Label 6025.161
Modulus $6025$
Conductor $6025$
Order $120$
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([96,29]))
 
pari: [g,chi] = znchar(Mod(161,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
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.il

\(\chi_{6025}(161,\cdot)\) \(\chi_{6025}(261,\cdot)\) \(\chi_{6025}(646,\cdot)\) \(\chi_{6025}(1396,\cdot)\) \(\chi_{6025}(1491,\cdot)\) \(\chi_{6025}(1496,\cdot)\) \(\chi_{6025}(1856,\cdot)\) \(\chi_{6025}(1916,\cdot)\) \(\chi_{6025}(1981,\cdot)\) \(\chi_{6025}(2166,\cdot)\) \(\chi_{6025}(2246,\cdot)\) \(\chi_{6025}(2381,\cdot)\) \(\chi_{6025}(2941,\cdot)\) \(\chi_{6025}(3356,\cdot)\) \(\chi_{6025}(3566,\cdot)\) \(\chi_{6025}(3836,\cdot)\) \(\chi_{6025}(3936,\cdot)\) \(\chi_{6025}(4271,\cdot)\) \(\chi_{6025}(4341,\cdot)\) \(\chi_{6025}(4356,\cdot)\) \(\chi_{6025}(4446,\cdot)\) \(\chi_{6025}(4471,\cdot)\) \(\chi_{6025}(4591,\cdot)\) \(\chi_{6025}(4646,\cdot)\) \(\chi_{6025}(4761,\cdot)\) \(\chi_{6025}(4986,\cdot)\) \(\chi_{6025}(5016,\cdot)\) \(\chi_{6025}(5136,\cdot)\) \(\chi_{6025}(5331,\cdot)\) \(\chi_{6025}(5361,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{29}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{101}{120}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{67}{120}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial