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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2365.dd
\(\chi_{2365}(47,\cdot)\) \(\chi_{2365}(97,\cdot)\) \(\chi_{2365}(102,\cdot)\) \(\chi_{2365}(207,\cdot)\) \(\chi_{2365}(213,\cdot)\) \(\chi_{2365}(262,\cdot)\) \(\chi_{2365}(312,\cdot)\) \(\chi_{2365}(317,\cdot)\) \(\chi_{2365}(322,\cdot)\) \(\chi_{2365}(422,\cdot)\) \(\chi_{2365}(477,\cdot)\) \(\chi_{2365}(532,\cdot)\) \(\chi_{2365}(537,\cdot)\) \(\chi_{2365}(643,\cdot)\) \(\chi_{2365}(742,\cdot)\) \(\chi_{2365}(752,\cdot)\) \(\chi_{2365}(828,\cdot)\) \(\chi_{2365}(852,\cdot)\) \(\chi_{2365}(907,\cdot)\) \(\chi_{2365}(938,\cdot)\) \(\chi_{2365}(962,\cdot)\) \(\chi_{2365}(993,\cdot)\) \(\chi_{2365}(1043,\cdot)\) \(\chi_{2365}(1048,\cdot)\) \(\chi_{2365}(1153,\cdot)\) \(\chi_{2365}(1182,\cdot)\) \(\chi_{2365}(1202,\cdot)\) \(\chi_{2365}(1208,\cdot)\) \(\chi_{2365}(1258,\cdot)\) \(\chi_{2365}(1263,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 2365 }(828, a) \) | \(-1\) | \(1\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{13}{70}\right)\) |