Properties

Label 6025.7
Modulus $6025$
Conductor $1205$
Order $240$
Real no
Primitive no
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([60,1]))
 
pari: [g,chi] = znchar(Mod(7,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(7,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.jp

\(\chi_{6025}(7,\cdot)\) \(\chi_{6025}(68,\cdot)\) \(\chi_{6025}(207,\cdot)\) \(\chi_{6025}(293,\cdot)\) \(\chi_{6025}(307,\cdot)\) \(\chi_{6025}(468,\cdot)\) \(\chi_{6025}(657,\cdot)\) \(\chi_{6025}(668,\cdot)\) \(\chi_{6025}(757,\cdot)\) \(\chi_{6025}(818,\cdot)\) \(\chi_{6025}(893,\cdot)\) \(\chi_{6025}(918,\cdot)\) \(\chi_{6025}(957,\cdot)\) \(\chi_{6025}(1218,\cdot)\) \(\chi_{6025}(1332,\cdot)\) \(\chi_{6025}(1368,\cdot)\) \(\chi_{6025}(1407,\cdot)\) \(\chi_{6025}(1532,\cdot)\) \(\chi_{6025}(1618,\cdot)\) \(\chi_{6025}(1718,\cdot)\) \(\chi_{6025}(1743,\cdot)\) \(\chi_{6025}(1757,\cdot)\) \(\chi_{6025}(1893,\cdot)\) \(\chi_{6025}(2032,\cdot)\) \(\chi_{6025}(2057,\cdot)\) \(\chi_{6025}(2107,\cdot)\) \(\chi_{6025}(2132,\cdot)\) \(\chi_{6025}(2243,\cdot)\) \(\chi_{6025}(2782,\cdot)\) \(\chi_{6025}(2818,\cdot)\) ...

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

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

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{61}{120}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{61}{240}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{71}{120}\right)\)\(e\left(\frac{227}{240}\right)\)
value at e.g. 2

Related number fields

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