Properties

Label 6025.52
Modulus $6025$
Conductor $6025$
Order $240$
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([12,187]))
 
pari: [g,chi] = znchar(Mod(52,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.iw

\(\chi_{6025}(52,\cdot)\) \(\chi_{6025}(172,\cdot)\) \(\chi_{6025}(387,\cdot)\) \(\chi_{6025}(447,\cdot)\) \(\chi_{6025}(537,\cdot)\) \(\chi_{6025}(548,\cdot)\) \(\chi_{6025}(613,\cdot)\) \(\chi_{6025}(653,\cdot)\) \(\chi_{6025}(667,\cdot)\) \(\chi_{6025}(677,\cdot)\) \(\chi_{6025}(692,\cdot)\) \(\chi_{6025}(878,\cdot)\) \(\chi_{6025}(898,\cdot)\) \(\chi_{6025}(913,\cdot)\) \(\chi_{6025}(977,\cdot)\) \(\chi_{6025}(1003,\cdot)\) \(\chi_{6025}(1163,\cdot)\) \(\chi_{6025}(1362,\cdot)\) \(\chi_{6025}(1488,\cdot)\) \(\chi_{6025}(1508,\cdot)\) \(\chi_{6025}(1558,\cdot)\) \(\chi_{6025}(1573,\cdot)\) \(\chi_{6025}(1722,\cdot)\) \(\chi_{6025}(1738,\cdot)\) \(\chi_{6025}(1942,\cdot)\) \(\chi_{6025}(1997,\cdot)\) \(\chi_{6025}(2012,\cdot)\) \(\chi_{6025}(2038,\cdot)\) \(\chi_{6025}(2247,\cdot)\) \(\chi_{6025}(2273,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{187}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{11}{120}\right)\)\(e\left(\frac{19}{120}\right)\)\(e\left(\frac{11}{60}\right)\)\(i\)\(e\left(\frac{7}{240}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{67}{240}\right)\)\(e\left(\frac{41}{120}\right)\)\(e\left(\frac{137}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial