Properties

Label 2601.44
Modulus $2601$
Conductor $867$
Order $272$
Real no
Primitive no
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(272))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([136,131]))
 
pari: [g,chi] = znchar(Mod(44,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(867\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(272\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{867}(44,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.bj

\(\chi_{2601}(44,\cdot)\) \(\chi_{2601}(62,\cdot)\) \(\chi_{2601}(71,\cdot)\) \(\chi_{2601}(80,\cdot)\) \(\chi_{2601}(107,\cdot)\) \(\chi_{2601}(116,\cdot)\) \(\chi_{2601}(125,\cdot)\) \(\chi_{2601}(143,\cdot)\) \(\chi_{2601}(197,\cdot)\) \(\chi_{2601}(215,\cdot)\) \(\chi_{2601}(233,\cdot)\) \(\chi_{2601}(260,\cdot)\) \(\chi_{2601}(269,\cdot)\) \(\chi_{2601}(278,\cdot)\) \(\chi_{2601}(296,\cdot)\) \(\chi_{2601}(350,\cdot)\) \(\chi_{2601}(368,\cdot)\) \(\chi_{2601}(377,\cdot)\) \(\chi_{2601}(386,\cdot)\) \(\chi_{2601}(413,\cdot)\) \(\chi_{2601}(422,\cdot)\) \(\chi_{2601}(431,\cdot)\) \(\chi_{2601}(449,\cdot)\) \(\chi_{2601}(521,\cdot)\) \(\chi_{2601}(530,\cdot)\) \(\chi_{2601}(539,\cdot)\) \(\chi_{2601}(566,\cdot)\) \(\chi_{2601}(575,\cdot)\) \(\chi_{2601}(584,\cdot)\) \(\chi_{2601}(602,\cdot)\) ...

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: $\Q(\zeta_{272})$
Fixed field: Number field defined by a degree 272 polynomial (not computed)

Values on generators

\((290,2026)\) → \((-1,e\left(\frac{131}{272}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{1}{136}\right)\)\(e\left(\frac{1}{68}\right)\)\(e\left(\frac{215}{272}\right)\)\(e\left(\frac{177}{272}\right)\)\(e\left(\frac{3}{136}\right)\)\(e\left(\frac{217}{272}\right)\)\(e\left(\frac{157}{272}\right)\)\(e\left(\frac{27}{68}\right)\)\(e\left(\frac{179}{272}\right)\)\(e\left(\frac{1}{34}\right)\)
value at e.g. 2