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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.bs
\(\chi_{8027}(3,\cdot)\) \(\chi_{8027}(4,\cdot)\) \(\chi_{8027}(29,\cdot)\) \(\chi_{8027}(49,\cdot)\) \(\chi_{8027}(73,\cdot)\) \(\chi_{8027}(78,\cdot)\) \(\chi_{8027}(95,\cdot)\) \(\chi_{8027}(104,\cdot)\) \(\chi_{8027}(124,\cdot)\) \(\chi_{8027}(142,\cdot)\) \(\chi_{8027}(164,\cdot)\) \(\chi_{8027}(169,\cdot)\) \(\chi_{8027}(202,\cdot)\) \(\chi_{8027}(233,\cdot)\) \(\chi_{8027}(238,\cdot)\) \(\chi_{8027}(243,\cdot)\) \(\chi_{8027}(255,\cdot)\) \(\chi_{8027}(262,\cdot)\) \(\chi_{8027}(324,\cdot)\) \(\chi_{8027}(326,\cdot)\) \(\chi_{8027}(330,\cdot)\) \(\chi_{8027}(334,\cdot)\) \(\chi_{8027}(335,\cdot)\) \(\chi_{8027}(340,\cdot)\) \(\chi_{8027}(353,\cdot)\) \(\chi_{8027}(354,\cdot)\) \(\chi_{8027}(371,\cdot)\) \(\chi_{8027}(422,\cdot)\) \(\chi_{8027}(427,\cdot)\) \(\chi_{8027}(432,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{957})$ |
Fixed field: | Number field defined by a degree 1914 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{5}{11}\right),e\left(\frac{79}{174}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(124, a) \) | \(1\) | \(1\) | \(e\left(\frac{695}{1914}\right)\) | \(e\left(\frac{74}{957}\right)\) | \(e\left(\frac{695}{957}\right)\) | \(e\left(\frac{17}{957}\right)\) | \(e\left(\frac{281}{638}\right)\) | \(e\left(\frac{107}{1914}\right)\) | \(e\left(\frac{57}{638}\right)\) | \(e\left(\frac{148}{957}\right)\) | \(e\left(\frac{243}{638}\right)\) | \(e\left(\frac{399}{638}\right)\) |