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.jm
\(\chi_{6048}(293,\cdot)\) \(\chi_{6048}(461,\cdot)\) \(\chi_{6048}(797,\cdot)\) \(\chi_{6048}(965,\cdot)\) \(\chi_{6048}(1301,\cdot)\) \(\chi_{6048}(1469,\cdot)\) \(\chi_{6048}(1805,\cdot)\) \(\chi_{6048}(1973,\cdot)\) \(\chi_{6048}(2309,\cdot)\) \(\chi_{6048}(2477,\cdot)\) \(\chi_{6048}(2813,\cdot)\) \(\chi_{6048}(2981,\cdot)\) \(\chi_{6048}(3317,\cdot)\) \(\chi_{6048}(3485,\cdot)\) \(\chi_{6048}(3821,\cdot)\) \(\chi_{6048}(3989,\cdot)\) \(\chi_{6048}(4325,\cdot)\) \(\chi_{6048}(4493,\cdot)\) \(\chi_{6048}(4829,\cdot)\) \(\chi_{6048}(4997,\cdot)\) \(\chi_{6048}(5333,\cdot)\) \(\chi_{6048}(5501,\cdot)\) \(\chi_{6048}(5837,\cdot)\) \(\chi_{6048}(6005,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4159,3781,3809,2593)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{7}{18}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 6048 }(965, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{24}\right)\) |