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.z
\(\chi_{8043}(2,\cdot)\) \(\chi_{8043}(23,\cdot)\) \(\chi_{8043}(32,\cdot)\) \(\chi_{8043}(65,\cdot)\) \(\chi_{8043}(86,\cdot)\) \(\chi_{8043}(116,\cdot)\) \(\chi_{8043}(128,\cdot)\) \(\chi_{8043}(137,\cdot)\) \(\chi_{8043}(149,\cdot)\) \(\chi_{8043}(200,\cdot)\) \(\chi_{8043}(242,\cdot)\) \(\chi_{8043}(263,\cdot)\) \(\chi_{8043}(284,\cdot)\) \(\chi_{8043}(305,\cdot)\) \(\chi_{8043}(317,\cdot)\) \(\chi_{8043}(338,\cdot)\) \(\chi_{8043}(368,\cdot)\) \(\chi_{8043}(389,\cdot)\) \(\chi_{8043}(401,\cdot)\) \(\chi_{8043}(410,\cdot)\) \(\chi_{8043}(431,\cdot)\) \(\chi_{8043}(452,\cdot)\) \(\chi_{8043}(464,\cdot)\) \(\chi_{8043}(485,\cdot)\) \(\chi_{8043}(527,\cdot)\) \(\chi_{8043}(536,\cdot)\) \(\chi_{8043}(548,\cdot)\) \(\chi_{8043}(557,\cdot)\) \(\chi_{8043}(569,\cdot)\) \(\chi_{8043}(578,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{119}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(65, a) \) | \(-1\) | \(1\) | \(e\left(\frac{749}{1146}\right)\) | \(e\left(\frac{176}{573}\right)\) | \(e\left(\frac{905}{1146}\right)\) | \(e\left(\frac{367}{382}\right)\) | \(e\left(\frac{254}{573}\right)\) | \(e\left(\frac{385}{1146}\right)\) | \(e\left(\frac{126}{191}\right)\) | \(e\left(\frac{352}{573}\right)\) | \(e\left(\frac{31}{1146}\right)\) | \(e\left(\frac{379}{573}\right)\) |