Basic properties
| Modulus: | \(8993\) | |
| Conductor: | \(8993\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(184\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8993.bb
\(\chi_{8993}(70,\cdot)\) \(\chi_{8993}(93,\cdot)\) \(\chi_{8993}(162,\cdot)\) \(\chi_{8993}(185,\cdot)\) \(\chi_{8993}(461,\cdot)\) \(\chi_{8993}(484,\cdot)\) \(\chi_{8993}(553,\cdot)\) \(\chi_{8993}(576,\cdot)\) \(\chi_{8993}(852,\cdot)\) \(\chi_{8993}(875,\cdot)\) \(\chi_{8993}(944,\cdot)\) \(\chi_{8993}(967,\cdot)\) \(\chi_{8993}(1243,\cdot)\) \(\chi_{8993}(1266,\cdot)\) \(\chi_{8993}(1335,\cdot)\) \(\chi_{8993}(1358,\cdot)\) \(\chi_{8993}(1634,\cdot)\) \(\chi_{8993}(1657,\cdot)\) \(\chi_{8993}(1726,\cdot)\) \(\chi_{8993}(1749,\cdot)\) \(\chi_{8993}(2025,\cdot)\) \(\chi_{8993}(2048,\cdot)\) \(\chi_{8993}(2140,\cdot)\) \(\chi_{8993}(2416,\cdot)\) \(\chi_{8993}(2439,\cdot)\) \(\chi_{8993}(2508,\cdot)\) \(\chi_{8993}(2531,\cdot)\) \(\chi_{8993}(2807,\cdot)\) \(\chi_{8993}(2830,\cdot)\) \(\chi_{8993}(2899,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{184})$ |
| Fixed field: | Number field defined by a degree 184 polynomial (not computed) |
Values on generators
\((530,7940)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{15}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8993 }(70, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{57}{184}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{5}{184}\right)\) | \(e\left(\frac{183}{184}\right)\) | \(e\left(\frac{139}{184}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{131}{184}\right)\) | \(e\left(\frac{175}{184}\right)\) |