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.ft
\(\chi_{3311}(74,\cdot)\) \(\chi_{3311}(310,\cdot)\) \(\chi_{3311}(354,\cdot)\) \(\chi_{3311}(359,\cdot)\) \(\chi_{3311}(382,\cdot)\) \(\chi_{3311}(541,\cdot)\) \(\chi_{3311}(611,\cdot)\) \(\chi_{3311}(655,\cdot)\) \(\chi_{3311}(711,\cdot)\) \(\chi_{3311}(744,\cdot)\) \(\chi_{3311}(842,\cdot)\) \(\chi_{3311}(877,\cdot)\) \(\chi_{3311}(970,\cdot)\) \(\chi_{3311}(1003,\cdot)\) \(\chi_{3311}(1201,\cdot)\) \(\chi_{3311}(1262,\cdot)\) \(\chi_{3311}(1271,\cdot)\) \(\chi_{3311}(1278,\cdot)\) \(\chi_{3311}(1304,\cdot)\) \(\chi_{3311}(1502,\cdot)\) \(\chi_{3311}(1514,\cdot)\) \(\chi_{3311}(1558,\cdot)\) \(\chi_{3311}(1579,\cdot)\) \(\chi_{3311}(1586,\cdot)\) \(\chi_{3311}(1614,\cdot)\) \(\chi_{3311}(1647,\cdot)\) \(\chi_{3311}(1745,\cdot)\) \(\chi_{3311}(1887,\cdot)\) \(\chi_{3311}(2081,\cdot)\) \(\chi_{3311}(2174,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{10}\right),e\left(\frac{17}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(74, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{43}{210}\right)\) |