Basic properties
| Modulus: | \(6026\) | |
| Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(286\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3013}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.z
\(\chi_{6026}(63,\cdot)\) \(\chi_{6026}(99,\cdot)\) \(\chi_{6026}(107,\cdot)\) \(\chi_{6026}(113,\cdot)\) \(\chi_{6026}(191,\cdot)\) \(\chi_{6026}(375,\cdot)\) \(\chi_{6026}(477,\cdot)\) \(\chi_{6026}(563,\cdot)\) \(\chi_{6026}(569,\cdot)\) \(\chi_{6026}(631,\cdot)\) \(\chi_{6026}(707,\cdot)\) \(\chi_{6026}(825,\cdot)\) \(\chi_{6026}(849,\cdot)\) \(\chi_{6026}(885,\cdot)\) \(\chi_{6026}(893,\cdot)\) \(\chi_{6026}(977,\cdot)\) \(\chi_{6026}(1029,\cdot)\) \(\chi_{6026}(1111,\cdot)\) \(\chi_{6026}(1147,\cdot)\) \(\chi_{6026}(1155,\cdot)\) \(\chi_{6026}(1161,\cdot)\) \(\chi_{6026}(1239,\cdot)\) \(\chi_{6026}(1259,\cdot)\) \(\chi_{6026}(1263,\cdot)\) \(\chi_{6026}(1349,\cdot)\) \(\chi_{6026}(1355,\cdot)\) \(\chi_{6026}(1417,\cdot)\) \(\chi_{6026}(1423,\cdot)\) \(\chi_{6026}(1493,\cdot)\) \(\chi_{6026}(1525,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{7}{22}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6026 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{69}{286}\right)\) | \(e\left(\frac{79}{286}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{71}{286}\right)\) | \(e\left(\frac{98}{143}\right)\) | \(e\left(\frac{73}{286}\right)\) | \(e\left(\frac{175}{286}\right)\) | \(e\left(\frac{111}{286}\right)\) | \(e\left(\frac{83}{286}\right)\) |