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Basic properties
| Modulus: | \(6223\) | |
| Conductor: | \(6223\) |
|
| Order: | \(21\) |
|
| Real: | no | |
| Primitive: | yes |
|
| Minimal: | yes | |
| Parity: | even |
|
Galois orbit 6223.de
\(\chi_{6223}(2,\cdot)\) \(\chi_{6223}(4,\cdot)\) \(\chi_{6223}(16,\cdot)\) \(\chi_{6223}(32,\cdot)\) \(\chi_{6223}(256,\cdot)\) \(\chi_{6223}(389,\cdot)\) \(\chi_{6223}(1024,\cdot)\) \(\chi_{6223}(1556,\cdot)\) \(\chi_{6223}(1969,\cdot)\) \(\chi_{6223}(2048,\cdot)\) \(\chi_{6223}(3112,\cdot)\) \(\chi_{6223}(3306,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{21})\) |
| Fixed field: | Number field defined by a degree 21 polynomial |
Values on generators
\((5589,638)\) → \((e\left(\frac{8}{21}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6223 }(3112, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |