Basic properties
Modulus: | \(4000\) | |
Conductor: | \(4000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.cz
\(\chi_{4000}(53,\cdot)\) \(\chi_{4000}(77,\cdot)\) \(\chi_{4000}(133,\cdot)\) \(\chi_{4000}(213,\cdot)\) \(\chi_{4000}(237,\cdot)\) \(\chi_{4000}(317,\cdot)\) \(\chi_{4000}(373,\cdot)\) \(\chi_{4000}(397,\cdot)\) \(\chi_{4000}(453,\cdot)\) \(\chi_{4000}(477,\cdot)\) \(\chi_{4000}(533,\cdot)\) \(\chi_{4000}(613,\cdot)\) \(\chi_{4000}(637,\cdot)\) \(\chi_{4000}(717,\cdot)\) \(\chi_{4000}(773,\cdot)\) \(\chi_{4000}(797,\cdot)\) \(\chi_{4000}(853,\cdot)\) \(\chi_{4000}(877,\cdot)\) \(\chi_{4000}(933,\cdot)\) \(\chi_{4000}(1013,\cdot)\) \(\chi_{4000}(1037,\cdot)\) \(\chi_{4000}(1117,\cdot)\) \(\chi_{4000}(1173,\cdot)\) \(\chi_{4000}(1197,\cdot)\) \(\chi_{4000}(1253,\cdot)\) \(\chi_{4000}(1277,\cdot)\) \(\chi_{4000}(1333,\cdot)\) \(\chi_{4000}(1413,\cdot)\) \(\chi_{4000}(1437,\cdot)\) \(\chi_{4000}(1517,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{19}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1413, a) \) | \(-1\) | \(1\) | \(e\left(\frac{141}{200}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{13}{200}\right)\) | \(e\left(\frac{57}{200}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{59}{200}\right)\) | \(e\left(\frac{21}{200}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{23}{200}\right)\) |