Properties

Label 6025.352
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([4,5]))
 
pari: [g,chi] = znchar(Mod(352,6025))
 

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.hc

\(\chi_{6025}(352,\cdot)\) \(\chi_{6025}(367,\cdot)\) \(\chi_{6025}(438,\cdot)\) \(\chi_{6025}(558,\cdot)\) \(\chi_{6025}(597,\cdot)\) \(\chi_{6025}(612,\cdot)\) \(\chi_{6025}(888,\cdot)\) \(\chi_{6025}(1008,\cdot)\) \(\chi_{6025}(1572,\cdot)\) \(\chi_{6025}(1763,\cdot)\) \(\chi_{6025}(1802,\cdot)\) \(\chi_{6025}(1817,\cdot)\) \(\chi_{6025}(2213,\cdot)\) \(\chi_{6025}(2762,\cdot)\) \(\chi_{6025}(2777,\cdot)\) \(\chi_{6025}(2848,\cdot)\) \(\chi_{6025}(3022,\cdot)\) \(\chi_{6025}(3298,\cdot)\) \(\chi_{6025}(3967,\cdot)\) \(\chi_{6025}(4053,\cdot)\) \(\chi_{6025}(4173,\cdot)\) \(\chi_{6025}(4212,\cdot)\) \(\chi_{6025}(4227,\cdot)\) \(\chi_{6025}(4503,\cdot)\) \(\chi_{6025}(4623,\cdot)\) \(\chi_{6025}(5172,\cdot)\) \(\chi_{6025}(5187,\cdot)\) \(\chi_{6025}(5258,\cdot)\) \(\chi_{6025}(5378,\cdot)\) \(\chi_{6025}(5417,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{1}{16}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{37}{40}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{71}{80}\right)\)
value at e.g. 2

Related number fields

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