Properties

Label 6025.33
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([12,69]))
 
pari: [g,chi] = znchar(Mod(33,6025))
 

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.hs

\(\chi_{6025}(33,\cdot)\) \(\chi_{6025}(198,\cdot)\) \(\chi_{6025}(208,\cdot)\) \(\chi_{6025}(267,\cdot)\) \(\chi_{6025}(503,\cdot)\) \(\chi_{6025}(587,\cdot)\) \(\chi_{6025}(1088,\cdot)\) \(\chi_{6025}(1102,\cdot)\) \(\chi_{6025}(1103,\cdot)\) \(\chi_{6025}(1188,\cdot)\) \(\chi_{6025}(1248,\cdot)\) \(\chi_{6025}(1463,\cdot)\) \(\chi_{6025}(1563,\cdot)\) \(\chi_{6025}(1602,\cdot)\) \(\chi_{6025}(2192,\cdot)\) \(\chi_{6025}(2708,\cdot)\) \(\chi_{6025}(2753,\cdot)\) \(\chi_{6025}(2787,\cdot)\) \(\chi_{6025}(2977,\cdot)\) \(\chi_{6025}(3273,\cdot)\) \(\chi_{6025}(3353,\cdot)\) \(\chi_{6025}(3447,\cdot)\) \(\chi_{6025}(3477,\cdot)\) \(\chi_{6025}(3522,\cdot)\) \(\chi_{6025}(3558,\cdot)\) \(\chi_{6025}(3587,\cdot)\) \(\chi_{6025}(3592,\cdot)\) \(\chi_{6025}(4198,\cdot)\) \(\chi_{6025}(4672,\cdot)\) \(\chi_{6025}(4747,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{69}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{49}{80}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{77}{80}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{31}{80}\right)\)
value at e.g. 2

Related number fields

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