Basic properties
| Modulus: | \(4000\) | |
| Conductor: | \(4000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | 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 4000.df
\(\chi_{4000}(67,\cdot)\) \(\chi_{4000}(123,\cdot)\) \(\chi_{4000}(147,\cdot)\) \(\chi_{4000}(203,\cdot)\) \(\chi_{4000}(227,\cdot)\) \(\chi_{4000}(283,\cdot)\) \(\chi_{4000}(363,\cdot)\) \(\chi_{4000}(387,\cdot)\) \(\chi_{4000}(467,\cdot)\) \(\chi_{4000}(523,\cdot)\) \(\chi_{4000}(547,\cdot)\) \(\chi_{4000}(603,\cdot)\) \(\chi_{4000}(627,\cdot)\) \(\chi_{4000}(683,\cdot)\) \(\chi_{4000}(763,\cdot)\) \(\chi_{4000}(787,\cdot)\) \(\chi_{4000}(867,\cdot)\) \(\chi_{4000}(923,\cdot)\) \(\chi_{4000}(947,\cdot)\) \(\chi_{4000}(1003,\cdot)\) \(\chi_{4000}(1027,\cdot)\) \(\chi_{4000}(1083,\cdot)\) \(\chi_{4000}(1163,\cdot)\) \(\chi_{4000}(1187,\cdot)\) \(\chi_{4000}(1267,\cdot)\) \(\chi_{4000}(1323,\cdot)\) \(\chi_{4000}(1347,\cdot)\) \(\chi_{4000}(1403,\cdot)\) \(\chi_{4000}(1427,\cdot)\) \(\chi_{4000}(1483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{200}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{51}{200}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{93}{200}\right)\) | \(e\left(\frac{167}{200}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{121}{200}\right)\) |