Basic properties
| Modulus: | \(6048\) | |
| Conductor: | \(6048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 6048.jq
\(\chi_{6048}(67,\cdot)\) \(\chi_{6048}(331,\cdot)\) \(\chi_{6048}(571,\cdot)\) \(\chi_{6048}(835,\cdot)\) \(\chi_{6048}(1075,\cdot)\) \(\chi_{6048}(1339,\cdot)\) \(\chi_{6048}(1579,\cdot)\) \(\chi_{6048}(1843,\cdot)\) \(\chi_{6048}(2083,\cdot)\) \(\chi_{6048}(2347,\cdot)\) \(\chi_{6048}(2587,\cdot)\) \(\chi_{6048}(2851,\cdot)\) \(\chi_{6048}(3091,\cdot)\) \(\chi_{6048}(3355,\cdot)\) \(\chi_{6048}(3595,\cdot)\) \(\chi_{6048}(3859,\cdot)\) \(\chi_{6048}(4099,\cdot)\) \(\chi_{6048}(4363,\cdot)\) \(\chi_{6048}(4603,\cdot)\) \(\chi_{6048}(4867,\cdot)\) \(\chi_{6048}(5107,\cdot)\) \(\chi_{6048}(5371,\cdot)\) \(\chi_{6048}(5611,\cdot)\) \(\chi_{6048}(5875,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{4}{9}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{3}{8}\right)\) |