Basic properties
| Modulus: | \(2793\) | |
| Conductor: | \(2793\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2793.ew
\(\chi_{2793}(143,\cdot)\) \(\chi_{2793}(173,\cdot)\) \(\chi_{2793}(299,\cdot)\) \(\chi_{2793}(383,\cdot)\) \(\chi_{2793}(395,\cdot)\) \(\chi_{2793}(542,\cdot)\) \(\chi_{2793}(572,\cdot)\) \(\chi_{2793}(698,\cdot)\) \(\chi_{2793}(773,\cdot)\) \(\chi_{2793}(782,\cdot)\) \(\chi_{2793}(794,\cdot)\) \(\chi_{2793}(941,\cdot)\) \(\chi_{2793}(971,\cdot)\) \(\chi_{2793}(1172,\cdot)\) \(\chi_{2793}(1181,\cdot)\) \(\chi_{2793}(1193,\cdot)\) \(\chi_{2793}(1340,\cdot)\) \(\chi_{2793}(1370,\cdot)\) \(\chi_{2793}(1496,\cdot)\) \(\chi_{2793}(1571,\cdot)\) \(\chi_{2793}(1580,\cdot)\) \(\chi_{2793}(1592,\cdot)\) \(\chi_{2793}(1739,\cdot)\) \(\chi_{2793}(1769,\cdot)\) \(\chi_{2793}(1895,\cdot)\) \(\chi_{2793}(1970,\cdot)\) \(\chi_{2793}(2168,\cdot)\) \(\chi_{2793}(2294,\cdot)\) \(\chi_{2793}(2369,\cdot)\) \(\chi_{2793}(2378,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{25}{42}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(2369, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) |