Basic properties
| Modulus: | \(2668\) | |
| Conductor: | \(2668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | 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 2668.bs
\(\chi_{2668}(3,\cdot)\) \(\chi_{2668}(27,\cdot)\) \(\chi_{2668}(31,\cdot)\) \(\chi_{2668}(39,\cdot)\) \(\chi_{2668}(55,\cdot)\) \(\chi_{2668}(95,\cdot)\) \(\chi_{2668}(119,\cdot)\) \(\chi_{2668}(127,\cdot)\) \(\chi_{2668}(131,\cdot)\) \(\chi_{2668}(147,\cdot)\) \(\chi_{2668}(163,\cdot)\) \(\chi_{2668}(211,\cdot)\) \(\chi_{2668}(243,\cdot)\) \(\chi_{2668}(259,\cdot)\) \(\chi_{2668}(271,\cdot)\) \(\chi_{2668}(279,\cdot)\) \(\chi_{2668}(311,\cdot)\) \(\chi_{2668}(351,\cdot)\) \(\chi_{2668}(363,\cdot)\) \(\chi_{2668}(395,\cdot)\) \(\chi_{2668}(403,\cdot)\) \(\chi_{2668}(427,\cdot)\) \(\chi_{2668}(443,\cdot)\) \(\chi_{2668}(491,\cdot)\) \(\chi_{2668}(495,\cdot)\) \(\chi_{2668}(519,\cdot)\) \(\chi_{2668}(583,\cdot)\) \(\chi_{2668}(591,\cdot)\) \(\chi_{2668}(607,\cdot)\) \(\chi_{2668}(611,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((1335,465,553)\) → \((-1,e\left(\frac{10}{11}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2668 }(403, a) \) | \(1\) | \(1\) | \(e\left(\frac{135}{308}\right)\) | \(e\left(\frac{129}{154}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{85}{308}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{75}{308}\right)\) | \(e\left(\frac{109}{308}\right)\) |