Basic properties
| Modulus: | \(2665\) | |
| Conductor: | \(2665\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 2665.hm
\(\chi_{2665}(22,\cdot)\) \(\chi_{2665}(48,\cdot)\) \(\chi_{2665}(198,\cdot)\) \(\chi_{2665}(302,\cdot)\) \(\chi_{2665}(347,\cdot)\) \(\chi_{2665}(432,\cdot)\) \(\chi_{2665}(438,\cdot)\) \(\chi_{2665}(458,\cdot)\) \(\chi_{2665}(477,\cdot)\) \(\chi_{2665}(503,\cdot)\) \(\chi_{2665}(757,\cdot)\) \(\chi_{2665}(848,\cdot)\) \(\chi_{2665}(867,\cdot)\) \(\chi_{2665}(887,\cdot)\) \(\chi_{2665}(913,\cdot)\) \(\chi_{2665}(1218,\cdot)\) \(\chi_{2665}(1277,\cdot)\) \(\chi_{2665}(1283,\cdot)\) \(\chi_{2665}(1452,\cdot)\) \(\chi_{2665}(1582,\cdot)\) \(\chi_{2665}(1628,\cdot)\) \(\chi_{2665}(1693,\cdot)\) \(\chi_{2665}(1862,\cdot)\) \(\chi_{2665}(1992,\cdot)\) \(\chi_{2665}(1998,\cdot)\) \(\chi_{2665}(2063,\cdot)\) \(\chi_{2665}(2167,\cdot)\) \(\chi_{2665}(2408,\cdot)\) \(\chi_{2665}(2453,\cdot)\) \(\chi_{2665}(2473,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1067,821,1236)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{29}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 2665 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |