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.jv
\(\chi_{6048}(11,\cdot)\) \(\chi_{6048}(275,\cdot)\) \(\chi_{6048}(515,\cdot)\) \(\chi_{6048}(779,\cdot)\) \(\chi_{6048}(1019,\cdot)\) \(\chi_{6048}(1283,\cdot)\) \(\chi_{6048}(1523,\cdot)\) \(\chi_{6048}(1787,\cdot)\) \(\chi_{6048}(2027,\cdot)\) \(\chi_{6048}(2291,\cdot)\) \(\chi_{6048}(2531,\cdot)\) \(\chi_{6048}(2795,\cdot)\) \(\chi_{6048}(3035,\cdot)\) \(\chi_{6048}(3299,\cdot)\) \(\chi_{6048}(3539,\cdot)\) \(\chi_{6048}(3803,\cdot)\) \(\chi_{6048}(4043,\cdot)\) \(\chi_{6048}(4307,\cdot)\) \(\chi_{6048}(4547,\cdot)\) \(\chi_{6048}(4811,\cdot)\) \(\chi_{6048}(5051,\cdot)\) \(\chi_{6048}(5315,\cdot)\) \(\chi_{6048}(5555,\cdot)\) \(\chi_{6048}(5819,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{7}{18}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(4043, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{24}\right)\) |