Properties

Label 2601.5
Modulus $2601$
Conductor $2601$
Order $816$
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(816))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([680,687]))
 
pari: [g,chi] = znchar(Mod(5,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(816\)
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.bn

\(\chi_{2601}(5,\cdot)\) \(\chi_{2601}(11,\cdot)\) \(\chi_{2601}(14,\cdot)\) \(\chi_{2601}(20,\cdot)\) \(\chi_{2601}(23,\cdot)\) \(\chi_{2601}(29,\cdot)\) \(\chi_{2601}(41,\cdot)\) \(\chi_{2601}(56,\cdot)\) \(\chi_{2601}(74,\cdot)\) \(\chi_{2601}(92,\cdot)\) \(\chi_{2601}(95,\cdot)\) \(\chi_{2601}(113,\cdot)\) \(\chi_{2601}(122,\cdot)\) \(\chi_{2601}(146,\cdot)\) \(\chi_{2601}(164,\cdot)\) \(\chi_{2601}(167,\cdot)\) \(\chi_{2601}(173,\cdot)\) \(\chi_{2601}(176,\cdot)\) \(\chi_{2601}(182,\cdot)\) \(\chi_{2601}(194,\cdot)\) \(\chi_{2601}(209,\cdot)\) \(\chi_{2601}(218,\cdot)\) \(\chi_{2601}(227,\cdot)\) \(\chi_{2601}(245,\cdot)\) \(\chi_{2601}(248,\cdot)\) \(\chi_{2601}(266,\cdot)\) \(\chi_{2601}(275,\cdot)\) \(\chi_{2601}(284,\cdot)\) \(\chi_{2601}(299,\cdot)\) \(\chi_{2601}(311,\cdot)\) ...

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: $\Q(\zeta_{816})$
Fixed field: Number field defined by a degree 816 polynomial (not computed)

Values on generators

\((290,2026)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{229}{272}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{325}{408}\right)\)\(e\left(\frac{121}{204}\right)\)\(e\left(\frac{787}{816}\right)\)\(e\left(\frac{677}{816}\right)\)\(e\left(\frac{53}{136}\right)\)\(e\left(\frac{207}{272}\right)\)\(e\left(\frac{161}{816}\right)\)\(e\left(\frac{139}{204}\right)\)\(e\left(\frac{511}{816}\right)\)\(e\left(\frac{19}{102}\right)\)
value at e.g. 2