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.jc
\(\chi_{6048}(13,\cdot)\) \(\chi_{6048}(349,\cdot)\) \(\chi_{6048}(517,\cdot)\) \(\chi_{6048}(853,\cdot)\) \(\chi_{6048}(1021,\cdot)\) \(\chi_{6048}(1357,\cdot)\) \(\chi_{6048}(1525,\cdot)\) \(\chi_{6048}(1861,\cdot)\) \(\chi_{6048}(2029,\cdot)\) \(\chi_{6048}(2365,\cdot)\) \(\chi_{6048}(2533,\cdot)\) \(\chi_{6048}(2869,\cdot)\) \(\chi_{6048}(3037,\cdot)\) \(\chi_{6048}(3373,\cdot)\) \(\chi_{6048}(3541,\cdot)\) \(\chi_{6048}(3877,\cdot)\) \(\chi_{6048}(4045,\cdot)\) \(\chi_{6048}(4381,\cdot)\) \(\chi_{6048}(4549,\cdot)\) \(\chi_{6048}(4885,\cdot)\) \(\chi_{6048}(5053,\cdot)\) \(\chi_{6048}(5389,\cdot)\) \(\chi_{6048}(5557,\cdot)\) \(\chi_{6048}(5893,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{4}{9}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{13}{24}\right)\) |