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.fs
\(\chi_{3311}(107,\cdot)\) \(\chi_{3311}(193,\cdot)\) \(\chi_{3311}(226,\cdot)\) \(\chi_{3311}(305,\cdot)\) \(\chi_{3311}(403,\cdot)\) \(\chi_{3311}(508,\cdot)\) \(\chi_{3311}(557,\cdot)\) \(\chi_{3311}(613,\cdot)\) \(\chi_{3311}(618,\cdot)\) \(\chi_{3311}(723,\cdot)\) \(\chi_{3311}(772,\cdot)\) \(\chi_{3311}(809,\cdot)\) \(\chi_{3311}(821,\cdot)\) \(\chi_{3311}(919,\cdot)\) \(\chi_{3311}(1073,\cdot)\) \(\chi_{3311}(1096,\cdot)\) \(\chi_{3311}(1129,\cdot)\) \(\chi_{3311}(1306,\cdot)\) \(\chi_{3311}(1311,\cdot)\) \(\chi_{3311}(1460,\cdot)\) \(\chi_{3311}(1509,\cdot)\) \(\chi_{3311}(1612,\cdot)\) \(\chi_{3311}(1712,\cdot)\) \(\chi_{3311}(1724,\cdot)\) \(\chi_{3311}(1810,\cdot)\) \(\chi_{3311}(1817,\cdot)\) \(\chi_{3311}(1822,\cdot)\) \(\chi_{3311}(1927,\cdot)\) \(\chi_{3311}(1976,\cdot)\) \(\chi_{3311}(1999,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{3}{10}\right),e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{210}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{51}{70}\right)\) |