Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(924\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 6003.dr
\(\chi_{6003}(11,\cdot)\) \(\chi_{6003}(14,\cdot)\) \(\chi_{6003}(56,\cdot)\) \(\chi_{6003}(113,\cdot)\) \(\chi_{6003}(155,\cdot)\) \(\chi_{6003}(176,\cdot)\) \(\chi_{6003}(182,\cdot)\) \(\chi_{6003}(218,\cdot)\) \(\chi_{6003}(221,\cdot)\) \(\chi_{6003}(263,\cdot)\) \(\chi_{6003}(272,\cdot)\) \(\chi_{6003}(293,\cdot)\) \(\chi_{6003}(329,\cdot)\) \(\chi_{6003}(356,\cdot)\) \(\chi_{6003}(362,\cdot)\) \(\chi_{6003}(398,\cdot)\) \(\chi_{6003}(425,\cdot)\) \(\chi_{6003}(479,\cdot)\) \(\chi_{6003}(536,\cdot)\) \(\chi_{6003}(569,\cdot)\) \(\chi_{6003}(572,\cdot)\) \(\chi_{6003}(590,\cdot)\) \(\chi_{6003}(617,\cdot)\) \(\chi_{6003}(635,\cdot)\) \(\chi_{6003}(641,\cdot)\) \(\chi_{6003}(659,\cdot)\) \(\chi_{6003}(677,\cdot)\) \(\chi_{6003}(686,\cdot)\) \(\chi_{6003}(704,\cdot)\) \(\chi_{6003}(707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{924})$ |
Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{21}{22}\right),e\left(\frac{13}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{924}\right)\) | \(e\left(\frac{191}{462}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{191}{308}\right)\) | \(e\left(\frac{167}{308}\right)\) | \(e\left(\frac{29}{924}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{229}{924}\right)\) | \(e\left(\frac{191}{231}\right)\) |