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.jf
\(\chi_{6048}(61,\cdot)\) \(\chi_{6048}(157,\cdot)\) \(\chi_{6048}(565,\cdot)\) \(\chi_{6048}(661,\cdot)\) \(\chi_{6048}(1069,\cdot)\) \(\chi_{6048}(1165,\cdot)\) \(\chi_{6048}(1573,\cdot)\) \(\chi_{6048}(1669,\cdot)\) \(\chi_{6048}(2077,\cdot)\) \(\chi_{6048}(2173,\cdot)\) \(\chi_{6048}(2581,\cdot)\) \(\chi_{6048}(2677,\cdot)\) \(\chi_{6048}(3085,\cdot)\) \(\chi_{6048}(3181,\cdot)\) \(\chi_{6048}(3589,\cdot)\) \(\chi_{6048}(3685,\cdot)\) \(\chi_{6048}(4093,\cdot)\) \(\chi_{6048}(4189,\cdot)\) \(\chi_{6048}(4597,\cdot)\) \(\chi_{6048}(4693,\cdot)\) \(\chi_{6048}(5101,\cdot)\) \(\chi_{6048}(5197,\cdot)\) \(\chi_{6048}(5605,\cdot)\) \(\chi_{6048}(5701,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{8}{9}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{3}{8}\right)\) |