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.dj
\(\chi_{6003}(7,\cdot)\) \(\chi_{6003}(103,\cdot)\) \(\chi_{6003}(112,\cdot)\) \(\chi_{6003}(268,\cdot)\) \(\chi_{6003}(286,\cdot)\) \(\chi_{6003}(310,\cdot)\) \(\chi_{6003}(313,\cdot)\) \(\chi_{6003}(355,\cdot)\) \(\chi_{6003}(364,\cdot)\) \(\chi_{6003}(373,\cdot)\) \(\chi_{6003}(517,\cdot)\) \(\chi_{6003}(571,\cdot)\) \(\chi_{6003}(661,\cdot)\) \(\chi_{6003}(778,\cdot)\) \(\chi_{6003}(799,\cdot)\) \(\chi_{6003}(835,\cdot)\) \(\chi_{6003}(895,\cdot)\) \(\chi_{6003}(1006,\cdot)\) \(\chi_{6003}(1069,\cdot)\) \(\chi_{6003}(1096,\cdot)\) \(\chi_{6003}(1138,\cdot)\) \(\chi_{6003}(1147,\cdot)\) \(\chi_{6003}(1183,\cdot)\) \(\chi_{6003}(1213,\cdot)\) \(\chi_{6003}(1321,\cdot)\) \(\chi_{6003}(1330,\cdot)\) \(\chi_{6003}(1354,\cdot)\) \(\chi_{6003}(1399,\cdot)\) \(\chi_{6003}(1408,\cdot)\) \(\chi_{6003}(1417,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{22}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6003 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{289}{462}\right)\) | \(e\left(\frac{101}{462}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{67}{231}\right)\) |