Basic properties
| Modulus: | \(1690\) | |
| Conductor: | \(13\) |
|
| Order: | \(3\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{13}(3,\cdot)\) |
|
| Minimal: | no | |
| Parity: | even |
|
Galois orbit 1690.e
\(\chi_{1690}(191,\cdot)\) \(\chi_{1690}(991,\cdot)\)
Related number fields
| Field of values: | \(\mathbb{Q}(\zeta_3)\) |
| Fixed field: | 3.3.169.1 |
Values on generators
\((677,171)\) → \((1,e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1690 }(991, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |