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.jo
\(\chi_{6048}(83,\cdot)\) \(\chi_{6048}(419,\cdot)\) \(\chi_{6048}(587,\cdot)\) \(\chi_{6048}(923,\cdot)\) \(\chi_{6048}(1091,\cdot)\) \(\chi_{6048}(1427,\cdot)\) \(\chi_{6048}(1595,\cdot)\) \(\chi_{6048}(1931,\cdot)\) \(\chi_{6048}(2099,\cdot)\) \(\chi_{6048}(2435,\cdot)\) \(\chi_{6048}(2603,\cdot)\) \(\chi_{6048}(2939,\cdot)\) \(\chi_{6048}(3107,\cdot)\) \(\chi_{6048}(3443,\cdot)\) \(\chi_{6048}(3611,\cdot)\) \(\chi_{6048}(3947,\cdot)\) \(\chi_{6048}(4115,\cdot)\) \(\chi_{6048}(4451,\cdot)\) \(\chi_{6048}(4619,\cdot)\) \(\chi_{6048}(4955,\cdot)\) \(\chi_{6048}(5123,\cdot)\) \(\chi_{6048}(5459,\cdot)\) \(\chi_{6048}(5627,\cdot)\) \(\chi_{6048}(5963,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{1}{18}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{24}\right)\) |