Properties

Label 6025.49
Modulus $6025$
Conductor $1205$
Order $120$
Real no
Primitive no
Minimal no
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([60,1]))
 
pari: [g,chi] = znchar(Mod(49,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(49,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.im

\(\chi_{6025}(49,\cdot)\) \(\chi_{6025}(174,\cdot)\) \(\chi_{6025}(349,\cdot)\) \(\chi_{6025}(374,\cdot)\) \(\chi_{6025}(549,\cdot)\) \(\chi_{6025}(674,\cdot)\) \(\chi_{6025}(1374,\cdot)\) \(\chi_{6025}(1449,\cdot)\) \(\chi_{6025}(1499,\cdot)\) \(\chi_{6025}(1699,\cdot)\) \(\chi_{6025}(1899,\cdot)\) \(\chi_{6025}(2124,\cdot)\) \(\chi_{6025}(2149,\cdot)\) \(\chi_{6025}(2249,\cdot)\) \(\chi_{6025}(2574,\cdot)\) \(\chi_{6025}(2874,\cdot)\) \(\chi_{6025}(3074,\cdot)\) \(\chi_{6025}(3299,\cdot)\) \(\chi_{6025}(3324,\cdot)\) \(\chi_{6025}(3424,\cdot)\) \(\chi_{6025}(3449,\cdot)\) \(\chi_{6025}(3674,\cdot)\) \(\chi_{6025}(3874,\cdot)\) \(\chi_{6025}(4174,\cdot)\) \(\chi_{6025}(4499,\cdot)\) \(\chi_{6025}(4599,\cdot)\) \(\chi_{6025}(4624,\cdot)\) \(\chi_{6025}(4849,\cdot)\) \(\chi_{6025}(5049,\cdot)\) \(\chi_{6025}(5249,\cdot)\) ...

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

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

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{61}{120}\right)\)\(i\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{107}{120}\right)\)
value at e.g. 2

Related number fields

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