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.de
\(\chi_{2365}(27,\cdot)\) \(\chi_{2365}(82,\cdot)\) \(\chi_{2365}(108,\cdot)\) \(\chi_{2365}(113,\cdot)\) \(\chi_{2365}(137,\cdot)\) \(\chi_{2365}(168,\cdot)\) \(\chi_{2365}(223,\cdot)\) \(\chi_{2365}(247,\cdot)\) \(\chi_{2365}(323,\cdot)\) \(\chi_{2365}(328,\cdot)\) \(\chi_{2365}(333,\cdot)\) \(\chi_{2365}(383,\cdot)\) \(\chi_{2365}(432,\cdot)\) \(\chi_{2365}(438,\cdot)\) \(\chi_{2365}(543,\cdot)\) \(\chi_{2365}(548,\cdot)\) \(\chi_{2365}(598,\cdot)\) \(\chi_{2365}(647,\cdot)\) \(\chi_{2365}(653,\cdot)\) \(\chi_{2365}(753,\cdot)\) \(\chi_{2365}(763,\cdot)\) \(\chi_{2365}(862,\cdot)\) \(\chi_{2365}(973,\cdot)\) \(\chi_{2365}(1028,\cdot)\) \(\chi_{2365}(1083,\cdot)\) \(\chi_{2365}(1193,\cdot)\) \(\chi_{2365}(1292,\cdot)\) \(\chi_{2365}(1312,\cdot)\) \(\chi_{2365}(1378,\cdot)\) \(\chi_{2365}(1527,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 2365 }(223, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) |