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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cy
\(\chi_{4000}(3,\cdot)\) \(\chi_{4000}(27,\cdot)\) \(\chi_{4000}(83,\cdot)\) \(\chi_{4000}(163,\cdot)\) \(\chi_{4000}(187,\cdot)\) \(\chi_{4000}(267,\cdot)\) \(\chi_{4000}(323,\cdot)\) \(\chi_{4000}(347,\cdot)\) \(\chi_{4000}(403,\cdot)\) \(\chi_{4000}(427,\cdot)\) \(\chi_{4000}(483,\cdot)\) \(\chi_{4000}(563,\cdot)\) \(\chi_{4000}(587,\cdot)\) \(\chi_{4000}(667,\cdot)\) \(\chi_{4000}(723,\cdot)\) \(\chi_{4000}(747,\cdot)\) \(\chi_{4000}(803,\cdot)\) \(\chi_{4000}(827,\cdot)\) \(\chi_{4000}(883,\cdot)\) \(\chi_{4000}(963,\cdot)\) \(\chi_{4000}(987,\cdot)\) \(\chi_{4000}(1067,\cdot)\) \(\chi_{4000}(1123,\cdot)\) \(\chi_{4000}(1147,\cdot)\) \(\chi_{4000}(1203,\cdot)\) \(\chi_{4000}(1227,\cdot)\) \(\chi_{4000}(1283,\cdot)\) \(\chi_{4000}(1363,\cdot)\) \(\chi_{4000}(1387,\cdot)\) \(\chi_{4000}(1467,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{83}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1283, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{200}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{91}{200}\right)\) | \(e\left(\frac{199}{200}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{13}{200}\right)\) | \(e\left(\frac{47}{200}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{61}{200}\right)\) |