Basic properties
| Modulus: | \(3311\) | |
| Conductor: | \(3311\) | 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 3311.fo
\(\chi_{3311}(19,\cdot)\) \(\chi_{3311}(73,\cdot)\) \(\chi_{3311}(206,\cdot)\) \(\chi_{3311}(458,\cdot)\) \(\chi_{3311}(579,\cdot)\) \(\chi_{3311}(607,\cdot)\) \(\chi_{3311}(635,\cdot)\) \(\chi_{3311}(717,\cdot)\) \(\chi_{3311}(843,\cdot)\) \(\chi_{3311}(908,\cdot)\) \(\chi_{3311}(915,\cdot)\) \(\chi_{3311}(976,\cdot)\) \(\chi_{3311}(992,\cdot)\) \(\chi_{3311}(1018,\cdot)\) \(\chi_{3311}(1179,\cdot)\) \(\chi_{3311}(1216,\cdot)\) \(\chi_{3311}(1223,\cdot)\) \(\chi_{3311}(1293,\cdot)\) \(\chi_{3311}(1361,\cdot)\) \(\chi_{3311}(1410,\cdot)\) \(\chi_{3311}(1480,\cdot)\) \(\chi_{3311}(1482,\cdot)\) \(\chi_{3311}(1524,\cdot)\) \(\chi_{3311}(1711,\cdot)\) \(\chi_{3311}(1746,\cdot)\) \(\chi_{3311}(1811,\cdot)\) \(\chi_{3311}(1839,\cdot)\) \(\chi_{3311}(1921,\cdot)\) \(\chi_{3311}(2119,\cdot)\) \(\chi_{3311}(2140,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{10}\right),e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{29}{105}\right)\) |