Properties

Label 6025.28
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([28,47]))
 
pari: [g,chi] = znchar(Mod(28,6025))
 

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.hr

\(\chi_{6025}(28,\cdot)\) \(\chi_{6025}(73,\cdot)\) \(\chi_{6025}(102,\cdot)\) \(\chi_{6025}(148,\cdot)\) \(\chi_{6025}(342,\cdot)\) \(\chi_{6025}(702,\cdot)\) \(\chi_{6025}(808,\cdot)\) \(\chi_{6025}(828,\cdot)\) \(\chi_{6025}(847,\cdot)\) \(\chi_{6025}(938,\cdot)\) \(\chi_{6025}(947,\cdot)\) \(\chi_{6025}(1222,\cdot)\) \(\chi_{6025}(1262,\cdot)\) \(\chi_{6025}(1298,\cdot)\) \(\chi_{6025}(1308,\cdot)\) \(\chi_{6025}(1322,\cdot)\) \(\chi_{6025}(1373,\cdot)\) \(\chi_{6025}(1713,\cdot)\) \(\chi_{6025}(2112,\cdot)\) \(\chi_{6025}(2367,\cdot)\) \(\chi_{6025}(3028,\cdot)\) \(\chi_{6025}(3417,\cdot)\) \(\chi_{6025}(3638,\cdot)\) \(\chi_{6025}(3828,\cdot)\) \(\chi_{6025}(3877,\cdot)\) \(\chi_{6025}(4477,\cdot)\) \(\chi_{6025}(4612,\cdot)\) \(\chi_{6025}(4787,\cdot)\) \(\chi_{6025}(4958,\cdot)\) \(\chi_{6025}(5038,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{47}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{27}{80}\right)\)\(e\left(\frac{37}{40}\right)\)\(-i\)\(e\left(\frac{23}{80}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{21}{80}\right)\)
value at e.g. 2

Related number fields

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