Properties

Label 6025.213
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([76,7]))
 
pari: [g,chi] = znchar(Mod(213,6025))
 

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.ht

\(\chi_{6025}(213,\cdot)\) \(\chi_{6025}(508,\cdot)\) \(\chi_{6025}(1278,\cdot)\) \(\chi_{6025}(1353,\cdot)\) \(\chi_{6025}(1827,\cdot)\) \(\chi_{6025}(2433,\cdot)\) \(\chi_{6025}(2438,\cdot)\) \(\chi_{6025}(2467,\cdot)\) \(\chi_{6025}(2503,\cdot)\) \(\chi_{6025}(2548,\cdot)\) \(\chi_{6025}(2578,\cdot)\) \(\chi_{6025}(2672,\cdot)\) \(\chi_{6025}(2752,\cdot)\) \(\chi_{6025}(3048,\cdot)\) \(\chi_{6025}(3238,\cdot)\) \(\chi_{6025}(3272,\cdot)\) \(\chi_{6025}(3317,\cdot)\) \(\chi_{6025}(3833,\cdot)\) \(\chi_{6025}(4423,\cdot)\) \(\chi_{6025}(4462,\cdot)\) \(\chi_{6025}(4562,\cdot)\) \(\chi_{6025}(4777,\cdot)\) \(\chi_{6025}(4837,\cdot)\) \(\chi_{6025}(4922,\cdot)\) \(\chi_{6025}(4923,\cdot)\) \(\chi_{6025}(4937,\cdot)\) \(\chi_{6025}(5438,\cdot)\) \(\chi_{6025}(5522,\cdot)\) \(\chi_{6025}(5758,\cdot)\) \(\chi_{6025}(5817,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{7}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{67}{80}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{31}{80}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{13}{80}\right)\)
value at e.g. 2

Related number fields

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