Properties

Label 6025.121
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([72,25]))
 
pari: [g,chi] = znchar(Mod(121,6025))
 

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.if

\(\chi_{6025}(121,\cdot)\) \(\chi_{6025}(361,\cdot)\) \(\chi_{6025}(691,\cdot)\) \(\chi_{6025}(721,\cdot)\) \(\chi_{6025}(836,\cdot)\) \(\chi_{6025}(966,\cdot)\) \(\chi_{6025}(996,\cdot)\) \(\chi_{6025}(1566,\cdot)\) \(\chi_{6025}(1896,\cdot)\) \(\chi_{6025}(2041,\cdot)\) \(\chi_{6025}(2056,\cdot)\) \(\chi_{6025}(2171,\cdot)\) \(\chi_{6025}(2531,\cdot)\) \(\chi_{6025}(2771,\cdot)\) \(\chi_{6025}(3131,\cdot)\) \(\chi_{6025}(3246,\cdot)\) \(\chi_{6025}(3261,\cdot)\) \(\chi_{6025}(3406,\cdot)\) \(\chi_{6025}(3736,\cdot)\) \(\chi_{6025}(4306,\cdot)\) \(\chi_{6025}(4336,\cdot)\) \(\chi_{6025}(4466,\cdot)\) \(\chi_{6025}(4581,\cdot)\) \(\chi_{6025}(4611,\cdot)\) \(\chi_{6025}(4941,\cdot)\) \(\chi_{6025}(5181,\cdot)\) \(\chi_{6025}(5511,\cdot)\) \(\chi_{6025}(5541,\cdot)\) \(\chi_{6025}(5656,\cdot)\) \(\chi_{6025}(5671,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{5}{24}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{97}{120}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{23}{120}\right)\)
value at e.g. 2

Related number fields

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