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.ga
\(\chi_{3311}(95,\cdot)\) \(\chi_{3311}(228,\cdot)\) \(\chi_{3311}(282,\cdot)\) \(\chi_{3311}(326,\cdot)\) \(\chi_{3311}(513,\cdot)\) \(\chi_{3311}(569,\cdot)\) \(\chi_{3311}(590,\cdot)\) \(\chi_{3311}(662,\cdot)\) \(\chi_{3311}(788,\cdot)\) \(\chi_{3311}(898,\cdot)\) \(\chi_{3311}(926,\cdot)\) \(\chi_{3311}(963,\cdot)\) \(\chi_{3311}(998,\cdot)\) \(\chi_{3311}(1047,\cdot)\) \(\chi_{3311}(1185,\cdot)\) \(\chi_{3311}(1227,\cdot)\) \(\chi_{3311}(1229,\cdot)\) \(\chi_{3311}(1348,\cdot)\) \(\chi_{3311}(1416,\cdot)\) \(\chi_{3311}(1432,\cdot)\) \(\chi_{3311}(1493,\cdot)\) \(\chi_{3311}(1691,\cdot)\) \(\chi_{3311}(1733,\cdot)\) \(\chi_{3311}(1773,\cdot)\) \(\chi_{3311}(1801,\cdot)\) \(\chi_{3311}(1866,\cdot)\) \(\chi_{3311}(2074,\cdot)\) \(\chi_{3311}(2130,\cdot)\) \(\chi_{3311}(2202,\cdot)\) \(\chi_{3311}(2251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{10}\right),e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{47}{210}\right)\) |