Basic properties
| Modulus: | \(1008\) | |
| Conductor: | \(56\) |
|
| Order: | \(6\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{56}(5,\cdot)\) |
|
| Minimal: | no | |
| Parity: | odd |
|
Galois orbit 1008.ce
\(\chi_{1008}(73,\cdot)\) \(\chi_{1008}(649,\cdot)\)
Related number fields
| Field of values: | \(\mathbb{Q}(\zeta_3)\) |
| Fixed field: | 6.0.8605184.1 |
Values on generators
\((127,757,785,577)\) → \((1,-1,1,e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 1008 }(649, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |