Basic properties
| Modulus: | \(15840\) | |
| Conductor: | \(55\) |
|
| Order: | \(20\) |
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{55}(28,\cdot)\) |
|
| Minimal: | yes | |
| Parity: | even |
|
Galois orbit 15840.ji
\(\chi_{15840}(2593,\cdot)\) \(\chi_{15840}(4033,\cdot)\) \(\chi_{15840}(4897,\cdot)\) \(\chi_{15840}(5473,\cdot)\) \(\chi_{15840}(11233,\cdot)\) \(\chi_{15840}(12097,\cdot)\) \(\chi_{15840}(13537,\cdot)\) \(\chi_{15840}(14977,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{20})\) |
| Fixed field: | \(\Q(\zeta_{55})^+\) |
Values on generators
\((991,13861,3521,6337,14401)\) → \((1,1,1,-i,e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 15840 }(5473, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-i\) |