Properties

Label 1441.46
Modulus $1441$
Conductor $1441$
Order $130$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1441, base_ring=CyclotomicField(130))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([13,24]))
 
pari: [g,chi] = znchar(Mod(46,1441))
 

Basic properties

Modulus: \(1441\)
Conductor: \(1441\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(130\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1441.bu

\(\chi_{1441}(46,\cdot)\) \(\chi_{1441}(74,\cdot)\) \(\chi_{1441}(94,\cdot)\) \(\chi_{1441}(101,\cdot)\) \(\chi_{1441}(138,\cdot)\) \(\chi_{1441}(222,\cdot)\) \(\chi_{1441}(282,\cdot)\) \(\chi_{1441}(303,\cdot)\) \(\chi_{1441}(370,\cdot)\) \(\chi_{1441}(371,\cdot)\) \(\chi_{1441}(391,\cdot)\) \(\chi_{1441}(409,\cdot)\) \(\chi_{1441}(414,\cdot)\) \(\chi_{1441}(448,\cdot)\) \(\chi_{1441}(457,\cdot)\) \(\chi_{1441}(470,\cdot)\) \(\chi_{1441}(514,\cdot)\) \(\chi_{1441}(557,\cdot)\) \(\chi_{1441}(568,\cdot)\) \(\chi_{1441}(629,\cdot)\) \(\chi_{1441}(666,\cdot)\) \(\chi_{1441}(690,\cdot)\) \(\chi_{1441}(789,\cdot)\) \(\chi_{1441}(799,\cdot)\) \(\chi_{1441}(811,\cdot)\) \(\chi_{1441}(909,\cdot)\) \(\chi_{1441}(921,\cdot)\) \(\chi_{1441}(926,\cdot)\) \(\chi_{1441}(976,\cdot)\) \(\chi_{1441}(992,\cdot)\) ...

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: $\Q(\zeta_{65})$
Fixed field: Number field defined by a degree 130 polynomial (not computed)

Values on generators

\((1311,133)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{12}{65}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\(-1\)\(1\)\(e\left(\frac{37}{130}\right)\)\(e\left(\frac{6}{65}\right)\)\(e\left(\frac{37}{65}\right)\)\(e\left(\frac{58}{65}\right)\)\(e\left(\frac{49}{130}\right)\)\(e\left(\frac{11}{26}\right)\)\(e\left(\frac{111}{130}\right)\)\(e\left(\frac{12}{65}\right)\)\(e\left(\frac{23}{130}\right)\)\(e\left(\frac{43}{65}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1441 }(46,a) \;\) at \(\;a = \) e.g. 2