Properties

Label 6025.29
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([12,77]))
 
pari: [g,chi] = znchar(Mod(29,6025))
 

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.ic

\(\chi_{6025}(29,\cdot)\) \(\chi_{6025}(59,\cdot)\) \(\chi_{6025}(429,\cdot)\) \(\chi_{6025}(554,\cdot)\) \(\chi_{6025}(884,\cdot)\) \(\chi_{6025}(984,\cdot)\) \(\chi_{6025}(1369,\cdot)\) \(\chi_{6025}(2119,\cdot)\) \(\chi_{6025}(2214,\cdot)\) \(\chi_{6025}(2219,\cdot)\) \(\chi_{6025}(2579,\cdot)\) \(\chi_{6025}(2639,\cdot)\) \(\chi_{6025}(2704,\cdot)\) \(\chi_{6025}(2889,\cdot)\) \(\chi_{6025}(2969,\cdot)\) \(\chi_{6025}(3104,\cdot)\) \(\chi_{6025}(3664,\cdot)\) \(\chi_{6025}(4079,\cdot)\) \(\chi_{6025}(4289,\cdot)\) \(\chi_{6025}(4559,\cdot)\) \(\chi_{6025}(4659,\cdot)\) \(\chi_{6025}(4994,\cdot)\) \(\chi_{6025}(5064,\cdot)\) \(\chi_{6025}(5079,\cdot)\) \(\chi_{6025}(5169,\cdot)\) \(\chi_{6025}(5194,\cdot)\) \(\chi_{6025}(5314,\cdot)\) \(\chi_{6025}(5369,\cdot)\) \(\chi_{6025}(5484,\cdot)\) \(\chi_{6025}(5709,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{77}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(-1\)\(e\left(\frac{17}{120}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{77}{120}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{7}{120}\right)\)
value at e.g. 2

Related number fields

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