Properties

Label 2601.25
Modulus $2601$
Conductor $2601$
Order $408$
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(408))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([272,279]))
 
pari: [g,chi] = znchar(Mod(25,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(2601\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(408\)
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.bk

\(\chi_{2601}(25,\cdot)\) \(\chi_{2601}(43,\cdot)\) \(\chi_{2601}(49,\cdot)\) \(\chi_{2601}(70,\cdot)\) \(\chi_{2601}(76,\cdot)\) \(\chi_{2601}(94,\cdot)\) \(\chi_{2601}(121,\cdot)\) \(\chi_{2601}(151,\cdot)\) \(\chi_{2601}(178,\cdot)\) \(\chi_{2601}(196,\cdot)\) \(\chi_{2601}(202,\cdot)\) \(\chi_{2601}(223,\cdot)\) \(\chi_{2601}(229,\cdot)\) \(\chi_{2601}(247,\cdot)\) \(\chi_{2601}(274,\cdot)\) \(\chi_{2601}(304,\cdot)\) \(\chi_{2601}(331,\cdot)\) \(\chi_{2601}(349,\cdot)\) \(\chi_{2601}(355,\cdot)\) \(\chi_{2601}(376,\cdot)\) \(\chi_{2601}(382,\cdot)\) \(\chi_{2601}(400,\cdot)\) \(\chi_{2601}(427,\cdot)\) \(\chi_{2601}(457,\cdot)\) \(\chi_{2601}(484,\cdot)\) \(\chi_{2601}(502,\cdot)\) \(\chi_{2601}(508,\cdot)\) \(\chi_{2601}(529,\cdot)\) \(\chi_{2601}(535,\cdot)\) \(\chi_{2601}(553,\cdot)\) ...

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: $\Q(\zeta_{408})$
Fixed field: Number field defined by a degree 408 polynomial (not computed)

Values on generators

\((290,2026)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{93}{136}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{121}{204}\right)\)\(e\left(\frac{19}{102}\right)\)\(e\left(\frac{379}{408}\right)\)\(e\left(\frac{269}{408}\right)\)\(e\left(\frac{53}{68}\right)\)\(e\left(\frac{71}{136}\right)\)\(e\left(\frac{161}{408}\right)\)\(e\left(\frac{37}{102}\right)\)\(e\left(\frac{103}{408}\right)\)\(e\left(\frac{19}{51}\right)\)
value at e.g. 2