Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.dl
\(\chi_{6003}(20,\cdot)\) \(\chi_{6003}(65,\cdot)\) \(\chi_{6003}(74,\cdot)\) \(\chi_{6003}(83,\cdot)\) \(\chi_{6003}(194,\cdot)\) \(\chi_{6003}(227,\cdot)\) \(\chi_{6003}(281,\cdot)\) \(\chi_{6003}(401,\cdot)\) \(\chi_{6003}(488,\cdot)\) \(\chi_{6003}(500,\cdot)\) \(\chi_{6003}(596,\cdot)\) \(\chi_{6003}(605,\cdot)\) \(\chi_{6003}(632,\cdot)\) \(\chi_{6003}(770,\cdot)\) \(\chi_{6003}(779,\cdot)\) \(\chi_{6003}(803,\cdot)\) \(\chi_{6003}(848,\cdot)\) \(\chi_{6003}(866,\cdot)\) \(\chi_{6003}(893,\cdot)\) \(\chi_{6003}(977,\cdot)\) \(\chi_{6003}(1010,\cdot)\) \(\chi_{6003}(1022,\cdot)\) \(\chi_{6003}(1031,\cdot)\) \(\chi_{6003}(1040,\cdot)\) \(\chi_{6003}(1109,\cdot)\) \(\chi_{6003}(1118,\cdot)\) \(\chi_{6003}(1184,\cdot)\) \(\chi_{6003}(1238,\cdot)\) \(\chi_{6003}(1325,\cdot)\) \(\chi_{6003}(1328,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{22}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1022, a) \) | \(1\) | \(1\) | \(e\left(\frac{247}{462}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{31}{462}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{32}{231}\right)\) |