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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.dn
\(\chi_{6003}(34,\cdot)\) \(\chi_{6003}(67,\cdot)\) \(\chi_{6003}(178,\cdot)\) \(\chi_{6003}(241,\cdot)\) \(\chi_{6003}(274,\cdot)\) \(\chi_{6003}(283,\cdot)\) \(\chi_{6003}(295,\cdot)\) \(\chi_{6003}(382,\cdot)\) \(\chi_{6003}(412,\cdot)\) \(\chi_{6003}(448,\cdot)\) \(\chi_{6003}(457,\cdot)\) \(\chi_{6003}(502,\cdot)\) \(\chi_{6003}(526,\cdot)\) \(\chi_{6003}(544,\cdot)\) \(\chi_{6003}(589,\cdot)\) \(\chi_{6003}(700,\cdot)\) \(\chi_{6003}(709,\cdot)\) \(\chi_{6003}(718,\cdot)\) \(\chi_{6003}(787,\cdot)\) \(\chi_{6003}(796,\cdot)\) \(\chi_{6003}(904,\cdot)\) \(\chi_{6003}(934,\cdot)\) \(\chi_{6003}(1078,\cdot)\) \(\chi_{6003}(1111,\cdot)\) \(\chi_{6003}(1165,\cdot)\) \(\chi_{6003}(1240,\cdot)\) \(\chi_{6003}(1282,\cdot)\) \(\chi_{6003}(1285,\cdot)\) \(\chi_{6003}(1309,\cdot)\) \(\chi_{6003}(1318,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{15}{22}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6003 }(709, a) \) | \(-1\) | \(1\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{160}{231}\right)\) |