Basic properties
| Modulus: | \(2365\) | |
| Conductor: | \(2365\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2365.dg
\(\chi_{2365}(107,\cdot)\) \(\chi_{2365}(127,\cdot)\) \(\chi_{2365}(183,\cdot)\) \(\chi_{2365}(193,\cdot)\) \(\chi_{2365}(293,\cdot)\) \(\chi_{2365}(348,\cdot)\) \(\chi_{2365}(398,\cdot)\) \(\chi_{2365}(403,\cdot)\) \(\chi_{2365}(508,\cdot)\) \(\chi_{2365}(557,\cdot)\) \(\chi_{2365}(563,\cdot)\) \(\chi_{2365}(613,\cdot)\) \(\chi_{2365}(618,\cdot)\) \(\chi_{2365}(623,\cdot)\) \(\chi_{2365}(723,\cdot)\) \(\chi_{2365}(772,\cdot)\) \(\chi_{2365}(778,\cdot)\) \(\chi_{2365}(833,\cdot)\) \(\chi_{2365}(838,\cdot)\) \(\chi_{2365}(987,\cdot)\) \(\chi_{2365}(1053,\cdot)\) \(\chi_{2365}(1073,\cdot)\) \(\chi_{2365}(1172,\cdot)\) \(\chi_{2365}(1282,\cdot)\) \(\chi_{2365}(1337,\cdot)\) \(\chi_{2365}(1392,\cdot)\) \(\chi_{2365}(1503,\cdot)\) \(\chi_{2365}(1602,\cdot)\) \(\chi_{2365}(1612,\cdot)\) \(\chi_{2365}(1712,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{3}{10}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 2365 }(1933, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) |