Basic properties
| Modulus: | \(2304\) | |
| Conductor: | \(96\) |
|
| Order: | \(8\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{96}(5,\cdot)\) |
|
| Minimal: | no | |
| Parity: | odd |
|
Galois orbit 2304.x
\(\chi_{2304}(161,\cdot)\) \(\chi_{2304}(737,\cdot)\) \(\chi_{2304}(1313,\cdot)\) \(\chi_{2304}(1889,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{8})\) |
| Fixed field: | 8.0.173946175488.1 |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{1}{8}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(737, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |