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.de
\(\chi_{4000}(13,\cdot)\) \(\chi_{4000}(37,\cdot)\) \(\chi_{4000}(117,\cdot)\) \(\chi_{4000}(173,\cdot)\) \(\chi_{4000}(197,\cdot)\) \(\chi_{4000}(253,\cdot)\) \(\chi_{4000}(277,\cdot)\) \(\chi_{4000}(333,\cdot)\) \(\chi_{4000}(413,\cdot)\) \(\chi_{4000}(437,\cdot)\) \(\chi_{4000}(517,\cdot)\) \(\chi_{4000}(573,\cdot)\) \(\chi_{4000}(597,\cdot)\) \(\chi_{4000}(653,\cdot)\) \(\chi_{4000}(677,\cdot)\) \(\chi_{4000}(733,\cdot)\) \(\chi_{4000}(813,\cdot)\) \(\chi_{4000}(837,\cdot)\) \(\chi_{4000}(917,\cdot)\) \(\chi_{4000}(973,\cdot)\) \(\chi_{4000}(997,\cdot)\) \(\chi_{4000}(1053,\cdot)\) \(\chi_{4000}(1077,\cdot)\) \(\chi_{4000}(1133,\cdot)\) \(\chi_{4000}(1213,\cdot)\) \(\chi_{4000}(1237,\cdot)\) \(\chi_{4000}(1317,\cdot)\) \(\chi_{4000}(1373,\cdot)\) \(\chi_{4000}(1397,\cdot)\) \(\chi_{4000}(1453,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{51}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1373, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{127}{200}\right)\) | \(e\left(\frac{103}{200}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{161}{200}\right)\) | \(e\left(\frac{159}{200}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{17}{200}\right)\) |