Properties

Label 6025.22
Modulus $6025$
Conductor $6025$
Order $240$
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([204,215]))
 
pari: [g,chi] = znchar(Mod(22,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.jn

\(\chi_{6025}(22,\cdot)\) \(\chi_{6025}(63,\cdot)\) \(\chi_{6025}(152,\cdot)\) \(\chi_{6025}(178,\cdot)\) \(\chi_{6025}(463,\cdot)\) \(\chi_{6025}(658,\cdot)\) \(\chi_{6025}(788,\cdot)\) \(\chi_{6025}(812,\cdot)\) \(\chi_{6025}(942,\cdot)\) \(\chi_{6025}(953,\cdot)\) \(\chi_{6025}(983,\cdot)\) \(\chi_{6025}(1002,\cdot)\) \(\chi_{6025}(1052,\cdot)\) \(\chi_{6025}(1117,\cdot)\) \(\chi_{6025}(1167,\cdot)\) \(\chi_{6025}(1227,\cdot)\) \(\chi_{6025}(1383,\cdot)\) \(\chi_{6025}(1698,\cdot)\) \(\chi_{6025}(1863,\cdot)\) \(\chi_{6025}(2017,\cdot)\) \(\chi_{6025}(2147,\cdot)\) \(\chi_{6025}(2158,\cdot)\) \(\chi_{6025}(2188,\cdot)\) \(\chi_{6025}(2322,\cdot)\) \(\chi_{6025}(2372,\cdot)\) \(\chi_{6025}(2473,\cdot)\) \(\chi_{6025}(2562,\cdot)\) \(\chi_{6025}(2588,\cdot)\) \(\chi_{6025}(2873,\cdot)\) \(\chi_{6025}(2903,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{43}{48}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{7}{120}\right)\)\(e\left(\frac{119}{120}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{239}{240}\right)\)\(e\left(\frac{13}{120}\right)\)\(e\left(\frac{61}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial