Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1914\) | 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 8027.br
\(\chi_{8027}(14,\cdot)\) \(\chi_{8027}(15,\cdot)\) \(\chi_{8027}(19,\cdot)\) \(\chi_{8027}(20,\cdot)\) \(\chi_{8027}(51,\cdot)\) \(\chi_{8027}(106,\cdot)\) \(\chi_{8027}(111,\cdot)\) \(\chi_{8027}(135,\cdot)\) \(\chi_{8027}(143,\cdot)\) \(\chi_{8027}(145,\cdot)\) \(\chi_{8027}(148,\cdot)\) \(\chi_{8027}(158,\cdot)\) \(\chi_{8027}(180,\cdot)\) \(\chi_{8027}(194,\cdot)\) \(\chi_{8027}(240,\cdot)\) \(\chi_{8027}(245,\cdot)\) \(\chi_{8027}(258,\cdot)\) \(\chi_{8027}(273,\cdot)\) \(\chi_{8027}(293,\cdot)\) \(\chi_{8027}(320,\cdot)\) \(\chi_{8027}(327,\cdot)\) \(\chi_{8027}(364,\cdot)\) \(\chi_{8027}(365,\cdot)\) \(\chi_{8027}(375,\cdot)\) \(\chi_{8027}(434,\cdot)\) \(\chi_{8027}(457,\cdot)\) \(\chi_{8027}(465,\cdot)\) \(\chi_{8027}(493,\cdot)\) \(\chi_{8027}(494,\cdot)\) \(\chi_{8027}(497,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{957})$ |
Fixed field: | Number field defined by a degree 1914 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{17}{22}\right),e\left(\frac{85}{87}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{500}{957}\right)\) | \(e\left(\frac{733}{957}\right)\) | \(e\left(\frac{43}{957}\right)\) | \(e\left(\frac{1061}{1914}\right)\) | \(e\left(\frac{92}{319}\right)\) | \(e\left(\frac{271}{1914}\right)\) | \(e\left(\frac{181}{319}\right)\) | \(e\left(\frac{509}{957}\right)\) | \(e\left(\frac{49}{638}\right)\) | \(e\left(\frac{301}{638}\right)\) |