Properties

Label 6025.138
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([76,63]))
 
pari: [g,chi] = znchar(Mod(138,6025))
 

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.hp

\(\chi_{6025}(138,\cdot)\) \(\chi_{6025}(638,\cdot)\) \(\chi_{6025}(997,\cdot)\) \(\chi_{6025}(1162,\cdot)\) \(\chi_{6025}(1172,\cdot)\) \(\chi_{6025}(1228,\cdot)\) \(\chi_{6025}(1467,\cdot)\) \(\chi_{6025}(1823,\cdot)\) \(\chi_{6025}(2013,\cdot)\) \(\chi_{6025}(2052,\cdot)\) \(\chi_{6025}(2067,\cdot)\) \(\chi_{6025}(2152,\cdot)\) \(\chi_{6025}(2212,\cdot)\) \(\chi_{6025}(2427,\cdot)\) \(\chi_{6025}(2483,\cdot)\) \(\chi_{6025}(2513,\cdot)\) \(\chi_{6025}(2527,\cdot)\) \(\chi_{6025}(2558,\cdot)\) \(\chi_{6025}(2623,\cdot)\) \(\chi_{6025}(2628,\cdot)\) \(\chi_{6025}(3672,\cdot)\) \(\chi_{6025}(3708,\cdot)\) \(\chi_{6025}(3717,\cdot)\) \(\chi_{6025}(3783,\cdot)\) \(\chi_{6025}(4237,\cdot)\) \(\chi_{6025}(4317,\cdot)\) \(\chi_{6025}(4522,\cdot)\) \(\chi_{6025}(4553,\cdot)\) \(\chi_{6025}(4848,\cdot)\) \(\chi_{6025}(5162,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{63}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{43}{80}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{71}{80}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{16}\right)\)
value at e.g. 2

Related number fields

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