Basic properties
| Modulus: | \(3751\) | |
| Conductor: | \(3751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 3751.cw
\(\chi_{3751}(95,\cdot)\) \(\chi_{3751}(101,\cdot)\) \(\chi_{3751}(140,\cdot)\) \(\chi_{3751}(314,\cdot)\) \(\chi_{3751}(436,\cdot)\) \(\chi_{3751}(442,\cdot)\) \(\chi_{3751}(655,\cdot)\) \(\chi_{3751}(777,\cdot)\) \(\chi_{3751}(783,\cdot)\) \(\chi_{3751}(822,\cdot)\) \(\chi_{3751}(996,\cdot)\) \(\chi_{3751}(1118,\cdot)\) \(\chi_{3751}(1124,\cdot)\) \(\chi_{3751}(1163,\cdot)\) \(\chi_{3751}(1337,\cdot)\) \(\chi_{3751}(1459,\cdot)\) \(\chi_{3751}(1465,\cdot)\) \(\chi_{3751}(1504,\cdot)\) \(\chi_{3751}(1678,\cdot)\) \(\chi_{3751}(1800,\cdot)\) \(\chi_{3751}(1845,\cdot)\) \(\chi_{3751}(2019,\cdot)\) \(\chi_{3751}(2141,\cdot)\) \(\chi_{3751}(2147,\cdot)\) \(\chi_{3751}(2186,\cdot)\) \(\chi_{3751}(2360,\cdot)\) \(\chi_{3751}(2482,\cdot)\) \(\chi_{3751}(2488,\cdot)\) \(\chi_{3751}(2527,\cdot)\) \(\chi_{3751}(2701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{47}{110}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) |