Basic properties
| Modulus: | \(8027\) | |
| Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3828\) | 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.bv
\(\chi_{8027}(2,\cdot)\) \(\chi_{8027}(13,\cdot)\) \(\chi_{8027}(18,\cdot)\) \(\chi_{8027}(32,\cdot)\) \(\chi_{8027}(50,\cdot)\) \(\chi_{8027}(54,\cdot)\) \(\chi_{8027}(55,\cdot)\) \(\chi_{8027}(59,\cdot)\) \(\chi_{8027}(62,\cdot)\) \(\chi_{8027}(71,\cdot)\) \(\chi_{8027}(72,\cdot)\) \(\chi_{8027}(82,\cdot)\) \(\chi_{8027}(96,\cdot)\) \(\chi_{8027}(105,\cdot)\) \(\chi_{8027}(117,\cdot)\) \(\chi_{8027}(119,\cdot)\) \(\chi_{8027}(128,\cdot)\) \(\chi_{8027}(140,\cdot)\) \(\chi_{8027}(141,\cdot)\) \(\chi_{8027}(150,\cdot)\) \(\chi_{8027}(154,\cdot)\) \(\chi_{8027}(156,\cdot)\) \(\chi_{8027}(165,\cdot)\) \(\chi_{8027}(173,\cdot)\) \(\chi_{8027}(174,\cdot)\) \(\chi_{8027}(177,\cdot)\) \(\chi_{8027}(188,\cdot)\) \(\chi_{8027}(190,\cdot)\) \(\chi_{8027}(193,\cdot)\) \(\chi_{8027}(197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3828})$ |
| Fixed field: | Number field defined by a degree 3828 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{7}{11}\right),e\left(\frac{271}{348}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8027 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{197}{3828}\right)\) | \(e\left(\frac{821}{1914}\right)\) | \(e\left(\frac{197}{1914}\right)\) | \(e\left(\frac{305}{1914}\right)\) | \(e\left(\frac{613}{1276}\right)\) | \(e\left(\frac{1019}{3828}\right)\) | \(e\left(\frac{197}{1276}\right)\) | \(e\left(\frac{821}{957}\right)\) | \(e\left(\frac{269}{1276}\right)\) | \(e\left(\frac{103}{1276}\right)\) |