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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.jg
\(\chi_{6048}(347,\cdot)\) \(\chi_{6048}(443,\cdot)\) \(\chi_{6048}(851,\cdot)\) \(\chi_{6048}(947,\cdot)\) \(\chi_{6048}(1355,\cdot)\) \(\chi_{6048}(1451,\cdot)\) \(\chi_{6048}(1859,\cdot)\) \(\chi_{6048}(1955,\cdot)\) \(\chi_{6048}(2363,\cdot)\) \(\chi_{6048}(2459,\cdot)\) \(\chi_{6048}(2867,\cdot)\) \(\chi_{6048}(2963,\cdot)\) \(\chi_{6048}(3371,\cdot)\) \(\chi_{6048}(3467,\cdot)\) \(\chi_{6048}(3875,\cdot)\) \(\chi_{6048}(3971,\cdot)\) \(\chi_{6048}(4379,\cdot)\) \(\chi_{6048}(4475,\cdot)\) \(\chi_{6048}(4883,\cdot)\) \(\chi_{6048}(4979,\cdot)\) \(\chi_{6048}(5387,\cdot)\) \(\chi_{6048}(5483,\cdot)\) \(\chi_{6048}(5891,\cdot)\) \(\chi_{6048}(5987,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{5}{18}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(4379, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{8}\right)\) |