Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(573\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2681}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.y
\(\chi_{8043}(4,\cdot)\) \(\chi_{8043}(16,\cdot)\) \(\chi_{8043}(25,\cdot)\) \(\chi_{8043}(46,\cdot)\) \(\chi_{8043}(58,\cdot)\) \(\chi_{8043}(67,\cdot)\) \(\chi_{8043}(100,\cdot)\) \(\chi_{8043}(121,\cdot)\) \(\chi_{8043}(130,\cdot)\) \(\chi_{8043}(142,\cdot)\) \(\chi_{8043}(172,\cdot)\) \(\chi_{8043}(184,\cdot)\) \(\chi_{8043}(193,\cdot)\) \(\chi_{8043}(205,\cdot)\) \(\chi_{8043}(226,\cdot)\) \(\chi_{8043}(235,\cdot)\) \(\chi_{8043}(256,\cdot)\) \(\chi_{8043}(268,\cdot)\) \(\chi_{8043}(277,\cdot)\) \(\chi_{8043}(289,\cdot)\) \(\chi_{8043}(298,\cdot)\) \(\chi_{8043}(331,\cdot)\) \(\chi_{8043}(361,\cdot)\) \(\chi_{8043}(373,\cdot)\) \(\chi_{8043}(415,\cdot)\) \(\chi_{8043}(445,\cdot)\) \(\chi_{8043}(499,\cdot)\) \(\chi_{8043}(520,\cdot)\) \(\chi_{8043}(529,\cdot)\) \(\chi_{8043}(583,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 573 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{134}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{197}{573}\right)\) | \(e\left(\frac{394}{573}\right)\) | \(e\left(\frac{20}{573}\right)\) | \(e\left(\frac{6}{191}\right)\) | \(e\left(\frac{217}{573}\right)\) | \(e\left(\frac{37}{573}\right)\) | \(e\left(\frac{52}{191}\right)\) | \(e\left(\frac{215}{573}\right)\) | \(e\left(\frac{64}{573}\right)\) | \(e\left(\frac{308}{573}\right)\) |