Basic properties
| Modulus: | \(8993\) | |
| Conductor: | \(8993\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2024\) | 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.bk
\(\chi_{8993}(2,\cdot)\) \(\chi_{8993}(8,\cdot)\) \(\chi_{8993}(9,\cdot)\) \(\chi_{8993}(25,\cdot)\) \(\chi_{8993}(26,\cdot)\) \(\chi_{8993}(32,\cdot)\) \(\chi_{8993}(36,\cdot)\) \(\chi_{8993}(49,\cdot)\) \(\chi_{8993}(59,\cdot)\) \(\chi_{8993}(77,\cdot)\) \(\chi_{8993}(87,\cdot)\) \(\chi_{8993}(94,\cdot)\) \(\chi_{8993}(100,\cdot)\) \(\chi_{8993}(104,\cdot)\) \(\chi_{8993}(110,\cdot)\) \(\chi_{8993}(117,\cdot)\) \(\chi_{8993}(121,\cdot)\) \(\chi_{8993}(127,\cdot)\) \(\chi_{8993}(128,\cdot)\) \(\chi_{8993}(144,\cdot)\) \(\chi_{8993}(151,\cdot)\) \(\chi_{8993}(179,\cdot)\) \(\chi_{8993}(196,\cdot)\) \(\chi_{8993}(202,\cdot)\) \(\chi_{8993}(213,\cdot)\) \(\chi_{8993}(219,\cdot)\) \(\chi_{8993}(223,\cdot)\) \(\chi_{8993}(236,\cdot)\) \(\chi_{8993}(246,\cdot)\) \(\chi_{8993}(257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2024})$ |
| Fixed field: | Number field defined by a degree 2024 polynomial (not computed) |
Values on generators
\((530,7940)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{100}{253}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8993 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{305}{1012}\right)\) | \(e\left(\frac{403}{2024}\right)\) | \(e\left(\frac{305}{506}\right)\) | \(e\left(\frac{1559}{2024}\right)\) | \(e\left(\frac{1013}{2024}\right)\) | \(e\left(\frac{1241}{2024}\right)\) | \(e\left(\frac{915}{1012}\right)\) | \(e\left(\frac{403}{1012}\right)\) | \(e\left(\frac{145}{2024}\right)\) | \(e\left(\frac{1205}{2024}\right)\) |