Properties

Label 6025.567
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([52,3]))
 
pari: [g,chi] = znchar(Mod(567,6025))
 

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.hq

\(\chi_{6025}(567,\cdot)\) \(\chi_{6025}(583,\cdot)\) \(\chi_{6025}(987,\cdot)\) \(\chi_{6025}(1067,\cdot)\) \(\chi_{6025}(1238,\cdot)\) \(\chi_{6025}(1413,\cdot)\) \(\chi_{6025}(1548,\cdot)\) \(\chi_{6025}(2148,\cdot)\) \(\chi_{6025}(2197,\cdot)\) \(\chi_{6025}(2387,\cdot)\) \(\chi_{6025}(2608,\cdot)\) \(\chi_{6025}(2997,\cdot)\) \(\chi_{6025}(3658,\cdot)\) \(\chi_{6025}(3913,\cdot)\) \(\chi_{6025}(4312,\cdot)\) \(\chi_{6025}(4652,\cdot)\) \(\chi_{6025}(4703,\cdot)\) \(\chi_{6025}(4717,\cdot)\) \(\chi_{6025}(4727,\cdot)\) \(\chi_{6025}(4763,\cdot)\) \(\chi_{6025}(4803,\cdot)\) \(\chi_{6025}(5078,\cdot)\) \(\chi_{6025}(5087,\cdot)\) \(\chi_{6025}(5178,\cdot)\) \(\chi_{6025}(5197,\cdot)\) \(\chi_{6025}(5217,\cdot)\) \(\chi_{6025}(5323,\cdot)\) \(\chi_{6025}(5683,\cdot)\) \(\chi_{6025}(5877,\cdot)\) \(\chi_{6025}(5923,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{3}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{23}{80}\right)\)\(e\left(\frac{13}{40}\right)\)\(-i\)\(e\left(\frac{27}{80}\right)\)\(e\left(\frac{37}{40}\right)\)\(e\left(\frac{9}{80}\right)\)
value at e.g. 2

Related number fields

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