Basic properties
| Modulus: | \(4006\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(286\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4006.n
\(\chi_{4006}(11,\cdot)\) \(\chi_{4006}(21,\cdot)\) \(\chi_{4006}(23,\cdot)\) \(\chi_{4006}(67,\cdot)\) \(\chi_{4006}(71,\cdot)\) \(\chi_{4006}(149,\cdot)\) \(\chi_{4006}(195,\cdot)\) \(\chi_{4006}(239,\cdot)\) \(\chi_{4006}(249,\cdot)\) \(\chi_{4006}(313,\cdot)\) \(\chi_{4006}(377,\cdot)\) \(\chi_{4006}(381,\cdot)\) \(\chi_{4006}(563,\cdot)\) \(\chi_{4006}(579,\cdot)\) \(\chi_{4006}(595,\cdot)\) \(\chi_{4006}(811,\cdot)\) \(\chi_{4006}(813,\cdot)\) \(\chi_{4006}(845,\cdot)\) \(\chi_{4006}(877,\cdot)\) \(\chi_{4006}(927,\cdot)\) \(\chi_{4006}(979,\cdot)\) \(\chi_{4006}(991,\cdot)\) \(\chi_{4006}(1079,\cdot)\) \(\chi_{4006}(1241,\cdot)\) \(\chi_{4006}(1249,\cdot)\) \(\chi_{4006}(1263,\cdot)\) \(\chi_{4006}(1275,\cdot)\) \(\chi_{4006}(1307,\cdot)\) \(\chi_{4006}(1331,\cdot)\) \(\chi_{4006}(1377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{7}{286}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4006 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{7}{286}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{57}{286}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{141}{286}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{24}{143}\right)\) | \(e\left(\frac{137}{286}\right)\) |