Basic properties
| Modulus: | \(6048\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{864}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.jp
\(\chi_{6048}(43,\cdot)\) \(\chi_{6048}(211,\cdot)\) \(\chi_{6048}(547,\cdot)\) \(\chi_{6048}(715,\cdot)\) \(\chi_{6048}(1051,\cdot)\) \(\chi_{6048}(1219,\cdot)\) \(\chi_{6048}(1555,\cdot)\) \(\chi_{6048}(1723,\cdot)\) \(\chi_{6048}(2059,\cdot)\) \(\chi_{6048}(2227,\cdot)\) \(\chi_{6048}(2563,\cdot)\) \(\chi_{6048}(2731,\cdot)\) \(\chi_{6048}(3067,\cdot)\) \(\chi_{6048}(3235,\cdot)\) \(\chi_{6048}(3571,\cdot)\) \(\chi_{6048}(3739,\cdot)\) \(\chi_{6048}(4075,\cdot)\) \(\chi_{6048}(4243,\cdot)\) \(\chi_{6048}(4579,\cdot)\) \(\chi_{6048}(4747,\cdot)\) \(\chi_{6048}(5083,\cdot)\) \(\chi_{6048}(5251,\cdot)\) \(\chi_{6048}(5587,\cdot)\) \(\chi_{6048}(5755,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{2}{9}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{23}{24}\right)\) |