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.fi
\(\chi_{3311}(94,\cdot)\) \(\chi_{3311}(194,\cdot)\) \(\chi_{3311}(376,\cdot)\) \(\chi_{3311}(409,\cdot)\) \(\chi_{3311}(481,\cdot)\) \(\chi_{3311}(591,\cdot)\) \(\chi_{3311}(677,\cdot)\) \(\chi_{3311}(684,\cdot)\) \(\chi_{3311}(710,\cdot)\) \(\chi_{3311}(733,\cdot)\) \(\chi_{3311}(887,\cdot)\) \(\chi_{3311}(899,\cdot)\) \(\chi_{3311}(948,\cdot)\) \(\chi_{3311}(985,\cdot)\) \(\chi_{3311}(997,\cdot)\) \(\chi_{3311}(1097,\cdot)\) \(\chi_{3311}(1102,\cdot)\) \(\chi_{3311}(1249,\cdot)\) \(\chi_{3311}(1403,\cdot)\) \(\chi_{3311}(1580,\cdot)\) \(\chi_{3311}(1613,\cdot)\) \(\chi_{3311}(1636,\cdot)\) \(\chi_{3311}(1685,\cdot)\) \(\chi_{3311}(1790,\cdot)\) \(\chi_{3311}(1795,\cdot)\) \(\chi_{3311}(1888,\cdot)\) \(\chi_{3311}(1900,\cdot)\) \(\chi_{3311}(1986,\cdot)\) \(\chi_{3311}(2096,\cdot)\) \(\chi_{3311}(2103,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{9}{10}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(94, a) \) | \(-1\) | \(1\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{4}{35}\right)\) |