Properties

Label 2601.16
Modulus $2601$
Conductor $2601$
Order $102$
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([68,81]))
 
pari: [g,chi] = znchar(Mod(16,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
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.bd

\(\chi_{2601}(16,\cdot)\) \(\chi_{2601}(67,\cdot)\) \(\chi_{2601}(169,\cdot)\) \(\chi_{2601}(220,\cdot)\) \(\chi_{2601}(322,\cdot)\) \(\chi_{2601}(373,\cdot)\) \(\chi_{2601}(475,\cdot)\) \(\chi_{2601}(526,\cdot)\) \(\chi_{2601}(628,\cdot)\) \(\chi_{2601}(679,\cdot)\) \(\chi_{2601}(781,\cdot)\) \(\chi_{2601}(832,\cdot)\) \(\chi_{2601}(934,\cdot)\) \(\chi_{2601}(985,\cdot)\) \(\chi_{2601}(1087,\cdot)\) \(\chi_{2601}(1138,\cdot)\) \(\chi_{2601}(1240,\cdot)\) \(\chi_{2601}(1291,\cdot)\) \(\chi_{2601}(1393,\cdot)\) \(\chi_{2601}(1546,\cdot)\) \(\chi_{2601}(1597,\cdot)\) \(\chi_{2601}(1699,\cdot)\) \(\chi_{2601}(1750,\cdot)\) \(\chi_{2601}(1852,\cdot)\) \(\chi_{2601}(1903,\cdot)\) \(\chi_{2601}(2005,\cdot)\) \(\chi_{2601}(2056,\cdot)\) \(\chi_{2601}(2158,\cdot)\) \(\chi_{2601}(2209,\cdot)\) \(\chi_{2601}(2362,\cdot)\) ...

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 102 polynomial (not computed)

Values on generators

\((290,2026)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{27}{34}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{28}{51}\right)\)\(e\left(\frac{5}{51}\right)\)\(e\left(\frac{19}{102}\right)\)\(e\left(\frac{77}{102}\right)\)\(e\left(\frac{11}{17}\right)\)\(e\left(\frac{25}{34}\right)\)\(e\left(\frac{95}{102}\right)\)\(e\left(\frac{50}{51}\right)\)\(e\left(\frac{31}{102}\right)\)\(e\left(\frac{10}{51}\right)\)
value at e.g. 2