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.fn
\(\chi_{3311}(47,\cdot)\) \(\chi_{3311}(59,\cdot)\) \(\chi_{3311}(213,\cdot)\) \(\chi_{3311}(236,\cdot)\) \(\chi_{3311}(262,\cdot)\) \(\chi_{3311}(269,\cdot)\) \(\chi_{3311}(355,\cdot)\) \(\chi_{3311}(465,\cdot)\) \(\chi_{3311}(537,\cdot)\) \(\chi_{3311}(570,\cdot)\) \(\chi_{3311}(752,\cdot)\) \(\chi_{3311}(852,\cdot)\) \(\chi_{3311}(950,\cdot)\) \(\chi_{3311}(962,\cdot)\) \(\chi_{3311}(1048,\cdot)\) \(\chi_{3311}(1116,\cdot)\) \(\chi_{3311}(1153,\cdot)\) \(\chi_{3311}(1202,\cdot)\) \(\chi_{3311}(1258,\cdot)\) \(\chi_{3311}(1263,\cdot)\) \(\chi_{3311}(1368,\cdot)\) \(\chi_{3311}(1417,\cdot)\) \(\chi_{3311}(1466,\cdot)\) \(\chi_{3311}(1655,\cdot)\) \(\chi_{3311}(1741,\cdot)\) \(\chi_{3311}(1774,\cdot)\) \(\chi_{3311}(1853,\cdot)\) \(\chi_{3311}(1951,\cdot)\) \(\chi_{3311}(1956,\cdot)\) \(\chi_{3311}(2105,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(1417, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{23}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{47}{70}\right)\) |