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 \(\chi_{864}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6048.jd
\(\chi_{6048}(29,\cdot)\) \(\chi_{6048}(365,\cdot)\) \(\chi_{6048}(533,\cdot)\) \(\chi_{6048}(869,\cdot)\) \(\chi_{6048}(1037,\cdot)\) \(\chi_{6048}(1373,\cdot)\) \(\chi_{6048}(1541,\cdot)\) \(\chi_{6048}(1877,\cdot)\) \(\chi_{6048}(2045,\cdot)\) \(\chi_{6048}(2381,\cdot)\) \(\chi_{6048}(2549,\cdot)\) \(\chi_{6048}(2885,\cdot)\) \(\chi_{6048}(3053,\cdot)\) \(\chi_{6048}(3389,\cdot)\) \(\chi_{6048}(3557,\cdot)\) \(\chi_{6048}(3893,\cdot)\) \(\chi_{6048}(4061,\cdot)\) \(\chi_{6048}(4397,\cdot)\) \(\chi_{6048}(4565,\cdot)\) \(\chi_{6048}(4901,\cdot)\) \(\chi_{6048}(5069,\cdot)\) \(\chi_{6048}(5405,\cdot)\) \(\chi_{6048}(5573,\cdot)\) \(\chi_{6048}(5909,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{1}{18}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{24}\right)\) |