Basic properties
| Modulus: | \(1775\) | |
| Conductor: | \(1775\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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 1775.cz
\(\chi_{1775}(12,\cdot)\) \(\chi_{1775}(77,\cdot)\) \(\chi_{1775}(148,\cdot)\) \(\chi_{1775}(178,\cdot)\) \(\chi_{1775}(228,\cdot)\) \(\chi_{1775}(313,\cdot)\) \(\chi_{1775}(358,\cdot)\) \(\chi_{1775}(363,\cdot)\) \(\chi_{1775}(438,\cdot)\) \(\chi_{1775}(577,\cdot)\) \(\chi_{1775}(578,\cdot)\) \(\chi_{1775}(608,\cdot)\) \(\chi_{1775}(642,\cdot)\) \(\chi_{1775}(648,\cdot)\) \(\chi_{1775}(658,\cdot)\) \(\chi_{1775}(677,\cdot)\) \(\chi_{1775}(697,\cdot)\) \(\chi_{1775}(737,\cdot)\) \(\chi_{1775}(748,\cdot)\) \(\chi_{1775}(783,\cdot)\) \(\chi_{1775}(797,\cdot)\) \(\chi_{1775}(892,\cdot)\) \(\chi_{1775}(902,\cdot)\) \(\chi_{1775}(927,\cdot)\) \(\chi_{1775}(942,\cdot)\) \(\chi_{1775}(947,\cdot)\) \(\chi_{1775}(973,\cdot)\) \(\chi_{1775}(983,\cdot)\) \(\chi_{1775}(998,\cdot)\) \(\chi_{1775}(1012,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((427,1001)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{19}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1775 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{101}{140}\right)\) |