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.fv
\(\chi_{3311}(114,\cdot)\) \(\chi_{3311}(163,\cdot)\) \(\chi_{3311}(235,\cdot)\) \(\chi_{3311}(291,\cdot)\) \(\chi_{3311}(499,\cdot)\) \(\chi_{3311}(564,\cdot)\) \(\chi_{3311}(592,\cdot)\) \(\chi_{3311}(632,\cdot)\) \(\chi_{3311}(674,\cdot)\) \(\chi_{3311}(872,\cdot)\) \(\chi_{3311}(933,\cdot)\) \(\chi_{3311}(949,\cdot)\) \(\chi_{3311}(1017,\cdot)\) \(\chi_{3311}(1136,\cdot)\) \(\chi_{3311}(1138,\cdot)\) \(\chi_{3311}(1180,\cdot)\) \(\chi_{3311}(1318,\cdot)\) \(\chi_{3311}(1367,\cdot)\) \(\chi_{3311}(1402,\cdot)\) \(\chi_{3311}(1439,\cdot)\) \(\chi_{3311}(1467,\cdot)\) \(\chi_{3311}(1577,\cdot)\) \(\chi_{3311}(1703,\cdot)\) \(\chi_{3311}(1775,\cdot)\) \(\chi_{3311}(1796,\cdot)\) \(\chi_{3311}(1852,\cdot)\) \(\chi_{3311}(2039,\cdot)\) \(\chi_{3311}(2083,\cdot)\) \(\chi_{3311}(2137,\cdot)\) \(\chi_{3311}(2270,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(114, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{105}\right)\) |