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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.ba
\(\chi_{8043}(5,\cdot)\) \(\chi_{8043}(26,\cdot)\) \(\chi_{8043}(47,\cdot)\) \(\chi_{8043}(59,\cdot)\) \(\chi_{8043}(80,\cdot)\) \(\chi_{8043}(89,\cdot)\) \(\chi_{8043}(122,\cdot)\) \(\chi_{8043}(131,\cdot)\) \(\chi_{8043}(164,\cdot)\) \(\chi_{8043}(194,\cdot)\) \(\chi_{8043}(215,\cdot)\) \(\chi_{8043}(236,\cdot)\) \(\chi_{8043}(257,\cdot)\) \(\chi_{8043}(269,\cdot)\) \(\chi_{8043}(290,\cdot)\) \(\chi_{8043}(299,\cdot)\) \(\chi_{8043}(311,\cdot)\) \(\chi_{8043}(320,\cdot)\) \(\chi_{8043}(332,\cdot)\) \(\chi_{8043}(341,\cdot)\) \(\chi_{8043}(362,\cdot)\) \(\chi_{8043}(374,\cdot)\) \(\chi_{8043}(416,\cdot)\) \(\chi_{8043}(488,\cdot)\) \(\chi_{8043}(500,\cdot)\) \(\chi_{8043}(542,\cdot)\) \(\chi_{8043}(563,\cdot)\) \(\chi_{8043}(593,\cdot)\) \(\chi_{8043}(605,\cdot)\) \(\chi_{8043}(614,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{145}{382}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{799}{1146}\right)\) | \(e\left(\frac{226}{573}\right)\) | \(e\left(\frac{817}{1146}\right)\) | \(e\left(\frac{35}{382}\right)\) | \(e\left(\frac{235}{573}\right)\) | \(e\left(\frac{283}{573}\right)\) | \(e\left(\frac{88}{191}\right)\) | \(e\left(\frac{452}{573}\right)\) | \(e\left(\frac{505}{573}\right)\) | \(e\left(\frac{205}{1146}\right)\) |