Properties

Label 6025.258
Modulus $6025$
Conductor $6025$
Order $80$
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([12,37]))
 
pari: [g,chi] = znchar(Mod(258,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(80\)
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.hm

\(\chi_{6025}(258,\cdot)\) \(\chi_{6025}(298,\cdot)\) \(\chi_{6025}(358,\cdot)\) \(\chi_{6025}(397,\cdot)\) \(\chi_{6025}(992,\cdot)\) \(\chi_{6025}(1037,\cdot)\) \(\chi_{6025}(1112,\cdot)\) \(\chi_{6025}(1148,\cdot)\) \(\chi_{6025}(1403,\cdot)\) \(\chi_{6025}(1772,\cdot)\) \(\chi_{6025}(1792,\cdot)\) \(\chi_{6025}(1902,\cdot)\) \(\chi_{6025}(2262,\cdot)\) \(\chi_{6025}(2272,\cdot)\) \(\chi_{6025}(2337,\cdot)\) \(\chi_{6025}(2453,\cdot)\) \(\chi_{6025}(2677,\cdot)\) \(\chi_{6025}(2913,\cdot)\) \(\chi_{6025}(3513,\cdot)\) \(\chi_{6025}(3648,\cdot)\) \(\chi_{6025}(3823,\cdot)\) \(\chi_{6025}(3992,\cdot)\) \(\chi_{6025}(4478,\cdot)\) \(\chi_{6025}(4602,\cdot)\) \(\chi_{6025}(4792,\cdot)\) \(\chi_{6025}(5163,\cdot)\) \(\chi_{6025}(5403,\cdot)\) \(\chi_{6025}(5763,\cdot)\) \(\chi_{6025}(5908,\cdot)\) \(\chi_{6025}(5922,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{37}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{9}{40}\right)\)\(e\left(\frac{1}{20}\right)\)\(i\)\(e\left(\frac{17}{80}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{77}{80}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{47}{80}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{80})$
Fixed field: Number field defined by a degree 80 polynomial