Properties

Label 6025.196
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([72,71]))
 
pari: [g,chi] = znchar(Mod(196,6025))
 

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.ig

\(\chi_{6025}(196,\cdot)\) \(\chi_{6025}(741,\cdot)\) \(\chi_{6025}(1716,\cdot)\) \(\chi_{6025}(1861,\cdot)\) \(\chi_{6025}(2036,\cdot)\) \(\chi_{6025}(2061,\cdot)\) \(\chi_{6025}(2116,\cdot)\) \(\chi_{6025}(2236,\cdot)\) \(\chi_{6025}(2241,\cdot)\) \(\chi_{6025}(2631,\cdot)\) \(\chi_{6025}(2696,\cdot)\) \(\chi_{6025}(2731,\cdot)\) \(\chi_{6025}(3121,\cdot)\) \(\chi_{6025}(3371,\cdot)\) \(\chi_{6025}(3556,\cdot)\) \(\chi_{6025}(3781,\cdot)\) \(\chi_{6025}(3931,\cdot)\) \(\chi_{6025}(4146,\cdot)\) \(\chi_{6025}(4156,\cdot)\) \(\chi_{6025}(4261,\cdot)\) \(\chi_{6025}(4266,\cdot)\) \(\chi_{6025}(4391,\cdot)\) \(\chi_{6025}(4771,\cdot)\) \(\chi_{6025}(4791,\cdot)\) \(\chi_{6025}(4981,\cdot)\) \(\chi_{6025}(5011,\cdot)\) \(\chi_{6025}(5081,\cdot)\) \(\chi_{6025}(5111,\cdot)\) \(\chi_{6025}(5546,\cdot)\) \(\chi_{6025}(5766,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{71}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{71}{120}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{47}{120}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{24}\right)\)
value at e.g. 2

Related number fields

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