Basic properties
| Modulus: | \(2394\) | |
| Conductor: | \(63\) |
|
| Order: | \(3\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{63}(58,\cdot)\) |
|
| Minimal: | yes | |
| Parity: | even |
|
Galois orbit 2394.i
\(\chi_{2394}(1255,\cdot)\) \(\chi_{2394}(2167,\cdot)\)
Related number fields
| Field of values: | \(\mathbb{Q}(\zeta_3)\) |
| Fixed field: | 3.3.3969.1 |
Values on generators
\((533,1711,1009)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{3}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2394 }(1255, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |