Basic properties
| Modulus: | \(3479\) | |
| Conductor: | \(3479\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 3479.fl
\(\chi_{3479}(102,\cdot)\) \(\chi_{3479}(130,\cdot)\) \(\chi_{3479}(186,\cdot)\) \(\chi_{3479}(347,\cdot)\) \(\chi_{3479}(352,\cdot)\) \(\chi_{3479}(487,\cdot)\) \(\chi_{3479}(550,\cdot)\) \(\chi_{3479}(562,\cdot)\) \(\chi_{3479}(564,\cdot)\) \(\chi_{3479}(590,\cdot)\) \(\chi_{3479}(695,\cdot)\) \(\chi_{3479}(772,\cdot)\) \(\chi_{3479}(779,\cdot)\) \(\chi_{3479}(914,\cdot)\) \(\chi_{3479}(954,\cdot)\) \(\chi_{3479}(1143,\cdot)\) \(\chi_{3479}(1199,\cdot)\) \(\chi_{3479}(1262,\cdot)\) \(\chi_{3479}(1313,\cdot)\) \(\chi_{3479}(1325,\cdot)\) \(\chi_{3479}(1360,\cdot)\) \(\chi_{3479}(1404,\cdot)\) \(\chi_{3479}(1418,\cdot)\) \(\chi_{3479}(1472,\cdot)\) \(\chi_{3479}(1502,\cdot)\) \(\chi_{3479}(1535,\cdot)\) \(\chi_{3479}(1661,\cdot)\) \(\chi_{3479}(1675,\cdot)\) \(\chi_{3479}(1726,\cdot)\) \(\chi_{3479}(1950,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((640,1569)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{11}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3479 }(102, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{62}{105}\right)\) |