Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(325\) | 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 8003.cd
\(\chi_{8003}(44,\cdot)\) \(\chi_{8003}(68,\cdot)\) \(\chi_{8003}(81,\cdot)\) \(\chi_{8003}(148,\cdot)\) \(\chi_{8003}(195,\cdot)\) \(\chi_{8003}(201,\cdot)\) \(\chi_{8003}(261,\cdot)\) \(\chi_{8003}(275,\cdot)\) \(\chi_{8003}(278,\cdot)\) \(\chi_{8003}(311,\cdot)\) \(\chi_{8003}(331,\cdot)\) \(\chi_{8003}(346,\cdot)\) \(\chi_{8003}(386,\cdot)\) \(\chi_{8003}(473,\cdot)\) \(\chi_{8003}(521,\cdot)\) \(\chi_{8003}(576,\cdot)\) \(\chi_{8003}(577,\cdot)\) \(\chi_{8003}(672,\cdot)\) \(\chi_{8003}(682,\cdot)\) \(\chi_{8003}(685,\cdot)\) \(\chi_{8003}(702,\cdot)\) \(\chi_{8003}(731,\cdot)\) \(\chi_{8003}(752,\cdot)\) \(\chi_{8003}(784,\cdot)\) \(\chi_{8003}(805,\cdot)\) \(\chi_{8003}(823,\cdot)\) \(\chi_{8003}(839,\cdot)\) \(\chi_{8003}(841,\cdot)\) \(\chi_{8003}(950,\cdot)\) \(\chi_{8003}(978,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{325})$ |
| Fixed field: | Number field defined by a degree 325 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{2}{13}\right),e\left(\frac{14}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{317}{325}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{309}{325}\right)\) | \(e\left(\frac{107}{325}\right)\) | \(e\left(\frac{219}{325}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{309}{325}\right)\) | \(e\left(\frac{99}{325}\right)\) | \(e\left(\frac{183}{325}\right)\) |