Basic properties
Modulus: | \(6010\) | |
Conductor: | \(3005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3005}(123,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.cs
\(\chi_{6010}(123,\cdot)\) \(\chi_{6010}(343,\cdot)\) \(\chi_{6010}(353,\cdot)\) \(\chi_{6010}(383,\cdot)\) \(\chi_{6010}(397,\cdot)\) \(\chi_{6010}(407,\cdot)\) \(\chi_{6010}(443,\cdot)\) \(\chi_{6010}(483,\cdot)\) \(\chi_{6010}(663,\cdot)\) \(\chi_{6010}(727,\cdot)\) \(\chi_{6010}(927,\cdot)\) \(\chi_{6010}(963,\cdot)\) \(\chi_{6010}(987,\cdot)\) \(\chi_{6010}(997,\cdot)\) \(\chi_{6010}(1027,\cdot)\) \(\chi_{6010}(1073,\cdot)\) \(\chi_{6010}(1093,\cdot)\) \(\chi_{6010}(1123,\cdot)\) \(\chi_{6010}(1233,\cdot)\) \(\chi_{6010}(1377,\cdot)\) \(\chi_{6010}(1383,\cdot)\) \(\chi_{6010}(1407,\cdot)\) \(\chi_{6010}(1417,\cdot)\) \(\chi_{6010}(1463,\cdot)\) \(\chi_{6010}(1473,\cdot)\) \(\chi_{6010}(1477,\cdot)\) \(\chi_{6010}(1593,\cdot)\) \(\chi_{6010}(1633,\cdot)\) \(\chi_{6010}(1677,\cdot)\) \(\chi_{6010}(1973,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((3607,2411)\) → \((-i,e\left(\frac{161}{200}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6010 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{111}{200}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{77}{200}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{101}{200}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{91}{100}\right)\) |