Basic properties
| Modulus: | \(3362\) | |
| Conductor: | \(41\) |
|
| Order: | \(5\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{41}(37,\cdot)\) |
|
| Minimal: | no | |
| Parity: | even |
|
Galois orbit 3362.d
\(\chi_{3362}(51,\cdot)\) \(\chi_{3362}(857,\cdot)\) \(\chi_{3362}(1533,\cdot)\) \(\chi_{3362}(2601,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{5})\) |
| Fixed field: | 5.5.2825761.1 |
Values on generators
\(1687\) → \(e\left(\frac{4}{5}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3362 }(857, a) \) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |