Basic properties
| Modulus: | \(3751\) | |
| Conductor: | \(3751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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.dx
\(\chi_{3751}(173,\cdot)\) \(\chi_{3751}(193,\cdot)\) \(\chi_{3751}(200,\cdot)\) \(\chi_{3751}(205,\cdot)\) \(\chi_{3751}(227,\cdot)\) \(\chi_{3751}(237,\cdot)\) \(\chi_{3751}(288,\cdot)\) \(\chi_{3751}(338,\cdot)\) \(\chi_{3751}(514,\cdot)\) \(\chi_{3751}(534,\cdot)\) \(\chi_{3751}(541,\cdot)\) \(\chi_{3751}(546,\cdot)\) \(\chi_{3751}(568,\cdot)\) \(\chi_{3751}(629,\cdot)\) \(\chi_{3751}(679,\cdot)\) \(\chi_{3751}(855,\cdot)\) \(\chi_{3751}(875,\cdot)\) \(\chi_{3751}(882,\cdot)\) \(\chi_{3751}(909,\cdot)\) \(\chi_{3751}(919,\cdot)\) \(\chi_{3751}(970,\cdot)\) \(\chi_{3751}(1020,\cdot)\) \(\chi_{3751}(1196,\cdot)\) \(\chi_{3751}(1216,\cdot)\) \(\chi_{3751}(1223,\cdot)\) \(\chi_{3751}(1228,\cdot)\) \(\chi_{3751}(1260,\cdot)\) \(\chi_{3751}(1311,\cdot)\) \(\chi_{3751}(1361,\cdot)\) \(\chi_{3751}(1537,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{103}{110}\right),e\left(\frac{13}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(173, a) \) | \(-1\) | \(1\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{122}{165}\right)\) |