Basic properties
| Modulus: | \(840\) | |
| Conductor: | \(28\) |
|
| Order: | \(6\) |
|
| Real: | no | |
| Primitive: | no, induced from 28.f |
|
| Minimal: | no | |
| Parity: | even |
|
Related number fields
| Field of values: | \(\mathbb{Q}(\zeta_3)\) |
| Fixed field: | \(\Q(\zeta_{28})^+\) |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{840}(31,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) |
| \(\chi_{840}(271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |