Basic properties
| Modulus: | \(4334\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2167}(1857,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.ba
\(\chi_{4334}(69,\cdot)\) \(\chi_{4334}(113,\cdot)\) \(\chi_{4334}(317,\cdot)\) \(\chi_{4334}(471,\cdot)\) \(\chi_{4334}(675,\cdot)\) \(\chi_{4334}(719,\cdot)\) \(\chi_{4334}(917,\cdot)\) \(\chi_{4334}(1005,\cdot)\) \(\chi_{4334}(1105,\cdot)\) \(\chi_{4334}(1259,\cdot)\) \(\chi_{4334}(1269,\cdot)\) \(\chi_{4334}(1489,\cdot)\) \(\chi_{4334}(1499,\cdot)\) \(\chi_{4334}(1653,\cdot)\) \(\chi_{4334}(1753,\cdot)\) \(\chi_{4334}(1841,\cdot)\) \(\chi_{4334}(1857,\cdot)\) \(\chi_{4334}(1901,\cdot)\) \(\chi_{4334}(2039,\cdot)\) \(\chi_{4334}(2083,\cdot)\) \(\chi_{4334}(2099,\cdot)\) \(\chi_{4334}(2187,\cdot)\) \(\chi_{4334}(2451,\cdot)\) \(\chi_{4334}(2645,\cdot)\) \(\chi_{4334}(2671,\cdot)\) \(\chi_{4334}(2689,\cdot)\) \(\chi_{4334}(2887,\cdot)\) \(\chi_{4334}(2935,\cdot)\) \(\chi_{4334}(2975,\cdot)\) \(\chi_{4334}(3023,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(1857, a) \) | \(-1\) | \(1\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) |