Basic properties
| Modulus: | \(4002\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(60,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bu
\(\chi_{4002}(19,\cdot)\) \(\chi_{4002}(37,\cdot)\) \(\chi_{4002}(43,\cdot)\) \(\chi_{4002}(61,\cdot)\) \(\chi_{4002}(79,\cdot)\) \(\chi_{4002}(97,\cdot)\) \(\chi_{4002}(205,\cdot)\) \(\chi_{4002}(217,\cdot)\) \(\chi_{4002}(235,\cdot)\) \(\chi_{4002}(247,\cdot)\) \(\chi_{4002}(337,\cdot)\) \(\chi_{4002}(379,\cdot)\) \(\chi_{4002}(385,\cdot)\) \(\chi_{4002}(421,\cdot)\) \(\chi_{4002}(433,\cdot)\) \(\chi_{4002}(475,\cdot)\) \(\chi_{4002}(511,\cdot)\) \(\chi_{4002}(559,\cdot)\) \(\chi_{4002}(595,\cdot)\) \(\chi_{4002}(619,\cdot)\) \(\chi_{4002}(649,\cdot)\) \(\chi_{4002}(727,\cdot)\) \(\chi_{4002}(733,\cdot)\) \(\chi_{4002}(751,\cdot)\) \(\chi_{4002}(757,\cdot)\) \(\chi_{4002}(769,\cdot)\) \(\chi_{4002}(793,\cdot)\) \(\chi_{4002}(889,\cdot)\) \(\chi_{4002}(907,\cdot)\) \(\chi_{4002}(925,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((1,e\left(\frac{21}{22}\right),e\left(\frac{1}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 4002 }(727, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{197}{308}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{235}{308}\right)\) | \(e\left(\frac{47}{154}\right)\) | \(e\left(\frac{47}{308}\right)\) |