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.jk
\(\chi_{6048}(205,\cdot)\) \(\chi_{6048}(445,\cdot)\) \(\chi_{6048}(709,\cdot)\) \(\chi_{6048}(949,\cdot)\) \(\chi_{6048}(1213,\cdot)\) \(\chi_{6048}(1453,\cdot)\) \(\chi_{6048}(1717,\cdot)\) \(\chi_{6048}(1957,\cdot)\) \(\chi_{6048}(2221,\cdot)\) \(\chi_{6048}(2461,\cdot)\) \(\chi_{6048}(2725,\cdot)\) \(\chi_{6048}(2965,\cdot)\) \(\chi_{6048}(3229,\cdot)\) \(\chi_{6048}(3469,\cdot)\) \(\chi_{6048}(3733,\cdot)\) \(\chi_{6048}(3973,\cdot)\) \(\chi_{6048}(4237,\cdot)\) \(\chi_{6048}(4477,\cdot)\) \(\chi_{6048}(4741,\cdot)\) \(\chi_{6048}(4981,\cdot)\) \(\chi_{6048}(5245,\cdot)\) \(\chi_{6048}(5485,\cdot)\) \(\chi_{6048}(5749,\cdot)\) \(\chi_{6048}(5989,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{8}{9}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(2221, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{8}\right)\) |