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.dg
\(\chi_{3751}(170,\cdot)\) \(\chi_{3751}(213,\cdot)\) \(\chi_{3751}(333,\cdot)\) \(\chi_{3751}(339,\cdot)\) \(\chi_{3751}(554,\cdot)\) \(\chi_{3751}(674,\cdot)\) \(\chi_{3751}(680,\cdot)\) \(\chi_{3751}(852,\cdot)\) \(\chi_{3751}(895,\cdot)\) \(\chi_{3751}(1015,\cdot)\) \(\chi_{3751}(1021,\cdot)\) \(\chi_{3751}(1193,\cdot)\) \(\chi_{3751}(1236,\cdot)\) \(\chi_{3751}(1356,\cdot)\) \(\chi_{3751}(1362,\cdot)\) \(\chi_{3751}(1534,\cdot)\) \(\chi_{3751}(1577,\cdot)\) \(\chi_{3751}(1875,\cdot)\) \(\chi_{3751}(1918,\cdot)\) \(\chi_{3751}(2038,\cdot)\) \(\chi_{3751}(2044,\cdot)\) \(\chi_{3751}(2216,\cdot)\) \(\chi_{3751}(2379,\cdot)\) \(\chi_{3751}(2385,\cdot)\) \(\chi_{3751}(2557,\cdot)\) \(\chi_{3751}(2600,\cdot)\) \(\chi_{3751}(2720,\cdot)\) \(\chi_{3751}(2726,\cdot)\) \(\chi_{3751}(2898,\cdot)\) \(\chi_{3751}(2941,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{2}{55}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(2557, a) \) | \(-1\) | \(1\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) |