Basic properties
| Modulus: | \(1083\) | |
| Conductor: | \(19\) |
|
| Order: | \(3\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{19}(7,\cdot)\) |
|
| Minimal: | no | |
| Parity: | even |
|
Galois orbit 1083.e
\(\chi_{1083}(292,\cdot)\) \(\chi_{1083}(790,\cdot)\)
Related number fields
| Field of values: | \(\mathbb{Q}(\zeta_3)\) |
| Fixed field: | 3.3.361.1 |
Values on generators
\((362,724)\) → \((1,e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1083 }(292, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |