Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | 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 6003.dh
\(\chi_{6003}(5,\cdot)\) \(\chi_{6003}(38,\cdot)\) \(\chi_{6003}(122,\cdot)\) \(\chi_{6003}(149,\cdot)\) \(\chi_{6003}(158,\cdot)\) \(\chi_{6003}(212,\cdot)\) \(\chi_{6003}(245,\cdot)\) \(\chi_{6003}(383,\cdot)\) \(\chi_{6003}(410,\cdot)\) \(\chi_{6003}(419,\cdot)\) \(\chi_{6003}(428,\cdot)\) \(\chi_{6003}(470,\cdot)\) \(\chi_{6003}(497,\cdot)\) \(\chi_{6003}(527,\cdot)\) \(\chi_{6003}(734,\cdot)\) \(\chi_{6003}(776,\cdot)\) \(\chi_{6003}(941,\cdot)\) \(\chi_{6003}(950,\cdot)\) \(\chi_{6003}(1019,\cdot)\) \(\chi_{6003}(1049,\cdot)\) \(\chi_{6003}(1193,\cdot)\) \(\chi_{6003}(1211,\cdot)\) \(\chi_{6003}(1253,\cdot)\) \(\chi_{6003}(1256,\cdot)\) \(\chi_{6003}(1280,\cdot)\) \(\chi_{6003}(1298,\cdot)\) \(\chi_{6003}(1397,\cdot)\) \(\chi_{6003}(1454,\cdot)\) \(\chi_{6003}(1463,\cdot)\) \(\chi_{6003}(1514,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{17}{22}\right),e\left(\frac{13}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1211, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{142}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{71}{77}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{1}{462}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{215}{462}\right)\) | \(e\left(\frac{53}{231}\right)\) |