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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.dc
\(\chi_{4000}(19,\cdot)\) \(\chi_{4000}(59,\cdot)\) \(\chi_{4000}(139,\cdot)\) \(\chi_{4000}(179,\cdot)\) \(\chi_{4000}(219,\cdot)\) \(\chi_{4000}(259,\cdot)\) \(\chi_{4000}(339,\cdot)\) \(\chi_{4000}(379,\cdot)\) \(\chi_{4000}(419,\cdot)\) \(\chi_{4000}(459,\cdot)\) \(\chi_{4000}(539,\cdot)\) \(\chi_{4000}(579,\cdot)\) \(\chi_{4000}(619,\cdot)\) \(\chi_{4000}(659,\cdot)\) \(\chi_{4000}(739,\cdot)\) \(\chi_{4000}(779,\cdot)\) \(\chi_{4000}(819,\cdot)\) \(\chi_{4000}(859,\cdot)\) \(\chi_{4000}(939,\cdot)\) \(\chi_{4000}(979,\cdot)\) \(\chi_{4000}(1019,\cdot)\) \(\chi_{4000}(1059,\cdot)\) \(\chi_{4000}(1139,\cdot)\) \(\chi_{4000}(1179,\cdot)\) \(\chi_{4000}(1219,\cdot)\) \(\chi_{4000}(1259,\cdot)\) \(\chi_{4000}(1339,\cdot)\) \(\chi_{4000}(1379,\cdot)\) \(\chi_{4000}(1419,\cdot)\) \(\chi_{4000}(1459,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{23}{50}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1539, a) \) | \(-1\) | \(1\) | \(e\left(\frac{169}{200}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{67}{200}\right)\) | \(e\left(\frac{113}{200}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{81}{200}\right)\) | \(e\left(\frac{39}{200}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{107}{200}\right)\) |