Properties

Label 6025.209
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([84,55]))
 
pari: [g,chi] = znchar(Mod(209,6025))
 

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.ie

\(\chi_{6025}(209,\cdot)\) \(\chi_{6025}(239,\cdot)\) \(\chi_{6025}(354,\cdot)\) \(\chi_{6025}(369,\cdot)\) \(\chi_{6025}(484,\cdot)\) \(\chi_{6025}(514,\cdot)\) \(\chi_{6025}(844,\cdot)\) \(\chi_{6025}(1084,\cdot)\) \(\chi_{6025}(1414,\cdot)\) \(\chi_{6025}(1444,\cdot)\) \(\chi_{6025}(1559,\cdot)\) \(\chi_{6025}(1689,\cdot)\) \(\chi_{6025}(1719,\cdot)\) \(\chi_{6025}(2289,\cdot)\) \(\chi_{6025}(2619,\cdot)\) \(\chi_{6025}(2764,\cdot)\) \(\chi_{6025}(2779,\cdot)\) \(\chi_{6025}(2894,\cdot)\) \(\chi_{6025}(3254,\cdot)\) \(\chi_{6025}(3494,\cdot)\) \(\chi_{6025}(3854,\cdot)\) \(\chi_{6025}(3969,\cdot)\) \(\chi_{6025}(3984,\cdot)\) \(\chi_{6025}(4129,\cdot)\) \(\chi_{6025}(4459,\cdot)\) \(\chi_{6025}(5029,\cdot)\) \(\chi_{6025}(5059,\cdot)\) \(\chi_{6025}(5189,\cdot)\) \(\chi_{6025}(5304,\cdot)\) \(\chi_{6025}(5334,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{11}{24}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{79}{120}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{101}{120}\right)\)
value at e.g. 2

Related number fields

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