Properties

Label 2601.52
Modulus $2601$
Conductor $2601$
Order $51$
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(102))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([68,12]))
 
pari: [g,chi] = znchar(Mod(52,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(51\)
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.y

\(\chi_{2601}(52,\cdot)\) \(\chi_{2601}(103,\cdot)\) \(\chi_{2601}(205,\cdot)\) \(\chi_{2601}(256,\cdot)\) \(\chi_{2601}(358,\cdot)\) \(\chi_{2601}(409,\cdot)\) \(\chi_{2601}(511,\cdot)\) \(\chi_{2601}(562,\cdot)\) \(\chi_{2601}(664,\cdot)\) \(\chi_{2601}(715,\cdot)\) \(\chi_{2601}(817,\cdot)\) \(\chi_{2601}(970,\cdot)\) \(\chi_{2601}(1021,\cdot)\) \(\chi_{2601}(1123,\cdot)\) \(\chi_{2601}(1174,\cdot)\) \(\chi_{2601}(1276,\cdot)\) \(\chi_{2601}(1327,\cdot)\) \(\chi_{2601}(1429,\cdot)\) \(\chi_{2601}(1480,\cdot)\) \(\chi_{2601}(1582,\cdot)\) \(\chi_{2601}(1633,\cdot)\) \(\chi_{2601}(1786,\cdot)\) \(\chi_{2601}(1888,\cdot)\) \(\chi_{2601}(1939,\cdot)\) \(\chi_{2601}(2041,\cdot)\) \(\chi_{2601}(2092,\cdot)\) \(\chi_{2601}(2194,\cdot)\) \(\chi_{2601}(2245,\cdot)\) \(\chi_{2601}(2347,\cdot)\) \(\chi_{2601}(2398,\cdot)\) ...

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: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 51 polynomial

Values on generators

\((290,2026)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{17}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{1}{51}\right)\)\(e\left(\frac{2}{51}\right)\)\(e\left(\frac{14}{51}\right)\)\(e\left(\frac{46}{51}\right)\)\(e\left(\frac{1}{17}\right)\)\(e\left(\frac{5}{17}\right)\)\(e\left(\frac{19}{51}\right)\)\(e\left(\frac{20}{51}\right)\)\(e\left(\frac{47}{51}\right)\)\(e\left(\frac{4}{51}\right)\)
value at e.g. 2