Basic properties
| Modulus: | \(1980\) | |
| Conductor: | \(11\) |
|
| Order: | \(5\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11}(4,\cdot)\) |
|
| Minimal: | yes | |
| Parity: | even |
|
Galois orbit 1980.z
\(\chi_{1980}(181,\cdot)\) \(\chi_{1980}(361,\cdot)\) \(\chi_{1980}(1081,\cdot)\) \(\chi_{1980}(1621,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{5})\) |
| Fixed field: | \(\Q(\zeta_{11})^+\) |
Values on generators
\((991,1541,397,541)\) → \((1,1,1,e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1980 }(1621, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |