Properties

Label 2601.4
Modulus $2601$
Conductor $2601$
Order $204$
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(2601, base_ring=CyclotomicField(204))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([68,81]))
 
pari: [g,chi] = znchar(Mod(4,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(204\)
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 2601.bg

\(\chi_{2601}(4,\cdot)\) \(\chi_{2601}(13,\cdot)\) \(\chi_{2601}(106,\cdot)\) \(\chi_{2601}(115,\cdot)\) \(\chi_{2601}(157,\cdot)\) \(\chi_{2601}(166,\cdot)\) \(\chi_{2601}(259,\cdot)\) \(\chi_{2601}(268,\cdot)\) \(\chi_{2601}(310,\cdot)\) \(\chi_{2601}(319,\cdot)\) \(\chi_{2601}(412,\cdot)\) \(\chi_{2601}(421,\cdot)\) \(\chi_{2601}(463,\cdot)\) \(\chi_{2601}(472,\cdot)\) \(\chi_{2601}(565,\cdot)\) \(\chi_{2601}(574,\cdot)\) \(\chi_{2601}(625,\cdot)\) \(\chi_{2601}(718,\cdot)\) \(\chi_{2601}(727,\cdot)\) \(\chi_{2601}(769,\cdot)\) \(\chi_{2601}(778,\cdot)\) \(\chi_{2601}(871,\cdot)\) \(\chi_{2601}(880,\cdot)\) \(\chi_{2601}(922,\cdot)\) \(\chi_{2601}(931,\cdot)\) \(\chi_{2601}(1024,\cdot)\) \(\chi_{2601}(1033,\cdot)\) \(\chi_{2601}(1075,\cdot)\) \(\chi_{2601}(1084,\cdot)\) \(\chi_{2601}(1177,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{204})$
Fixed field: Number field defined by a degree 204 polynomial (not computed)

Values on generators

\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{27}{68}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{79}{102}\right)\)\(e\left(\frac{28}{51}\right)\)\(e\left(\frac{121}{204}\right)\)\(e\left(\frac{179}{204}\right)\)\(e\left(\frac{11}{34}\right)\)\(e\left(\frac{25}{68}\right)\)\(e\left(\frac{95}{204}\right)\)\(e\left(\frac{25}{51}\right)\)\(e\left(\frac{133}{204}\right)\)\(e\left(\frac{5}{51}\right)\)
value at e.g. 2