Basic properties
| Modulus: | \(8664\) | |
| Conductor: | \(19\) |
|
| Order: | \(9\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{19}(17,\cdot)\) |
|
| Minimal: | no | |
| Parity: | even |
|
Galois orbit 8664.bg
\(\chi_{8664}(2761,\cdot)\) \(\chi_{8664}(4033,\cdot)\) \(\chi_{8664}(6913,\cdot)\) \(\chi_{8664}(7465,\cdot)\) \(\chi_{8664}(7609,\cdot)\) \(\chi_{8664}(8041,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{9})\) |
| Fixed field: | \(\Q(\zeta_{19})^+\) |
Values on generators
\((2167,4333,5777,8305)\) → \((1,1,1,e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8664 }(7465, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) |