Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(8043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1146\) | 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 8043.bb
\(\chi_{8043}(17,\cdot)\) \(\chi_{8043}(38,\cdot)\) \(\chi_{8043}(68,\cdot)\) \(\chi_{8043}(101,\cdot)\) \(\chi_{8043}(110,\cdot)\) \(\chi_{8043}(143,\cdot)\) \(\chi_{8043}(152,\cdot)\) \(\chi_{8043}(173,\cdot)\) \(\chi_{8043}(185,\cdot)\) \(\chi_{8043}(206,\cdot)\) \(\chi_{8043}(227,\cdot)\) \(\chi_{8043}(248,\cdot)\) \(\chi_{8043}(278,\cdot)\) \(\chi_{8043}(353,\cdot)\) \(\chi_{8043}(395,\cdot)\) \(\chi_{8043}(404,\cdot)\) \(\chi_{8043}(425,\cdot)\) \(\chi_{8043}(437,\cdot)\) \(\chi_{8043}(446,\cdot)\) \(\chi_{8043}(458,\cdot)\) \(\chi_{8043}(467,\cdot)\) \(\chi_{8043}(479,\cdot)\) \(\chi_{8043}(509,\cdot)\) \(\chi_{8043}(521,\cdot)\) \(\chi_{8043}(530,\cdot)\) \(\chi_{8043}(551,\cdot)\) \(\chi_{8043}(572,\cdot)\) \(\chi_{8043}(584,\cdot)\) \(\chi_{8043}(626,\cdot)\) \(\chi_{8043}(635,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{76}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(353, a) \) | \(1\) | \(1\) | \(e\left(\frac{175}{1146}\right)\) | \(e\left(\frac{175}{573}\right)\) | \(e\left(\frac{419}{573}\right)\) | \(e\left(\frac{175}{382}\right)\) | \(e\left(\frac{1013}{1146}\right)\) | \(e\left(\frac{347}{1146}\right)\) | \(e\left(\frac{307}{382}\right)\) | \(e\left(\frac{350}{573}\right)\) | \(e\left(\frac{424}{573}\right)\) | \(e\left(\frac{643}{1146}\right)\) |