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.gd
\(\chi_{3311}(146,\cdot)\) \(\chi_{3311}(181,\cdot)\) \(\chi_{3311}(412,\cdot)\) \(\chi_{3311}(454,\cdot)\) \(\chi_{3311}(482,\cdot)\) \(\chi_{3311}(531,\cdot)\) \(\chi_{3311}(685,\cdot)\) \(\chi_{3311}(713,\cdot)\) \(\chi_{3311}(741,\cdot)\) \(\chi_{3311}(762,\cdot)\) \(\chi_{3311}(797,\cdot)\) \(\chi_{3311}(874,\cdot)\) \(\chi_{3311}(916,\cdot)\) \(\chi_{3311}(1049,\cdot)\) \(\chi_{3311}(1070,\cdot)\) \(\chi_{3311}(1098,\cdot)\) \(\chi_{3311}(1175,\cdot)\) \(\chi_{3311}(1357,\cdot)\) \(\chi_{3311}(1434,\cdot)\) \(\chi_{3311}(1588,\cdot)\) \(\chi_{3311}(1644,\cdot)\) \(\chi_{3311}(1665,\cdot)\) \(\chi_{3311}(1686,\cdot)\) \(\chi_{3311}(1819,\cdot)\) \(\chi_{3311}(1917,\cdot)\) \(\chi_{3311}(1945,\cdot)\) \(\chi_{3311}(1952,\cdot)\) \(\chi_{3311}(1973,\cdot)\) \(\chi_{3311}(2253,\cdot)\) \(\chi_{3311}(2260,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(146, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{53}{210}\right)\) |