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.dr
\(\chi_{3751}(50,\cdot)\) \(\chi_{3751}(72,\cdot)\) \(\chi_{3751}(90,\cdot)\) \(\chi_{3751}(162,\cdot)\) \(\chi_{3751}(206,\cdot)\) \(\chi_{3751}(266,\cdot)\) \(\chi_{3751}(293,\cdot)\) \(\chi_{3751}(381,\cdot)\) \(\chi_{3751}(391,\cdot)\) \(\chi_{3751}(413,\cdot)\) \(\chi_{3751}(431,\cdot)\) \(\chi_{3751}(503,\cdot)\) \(\chi_{3751}(547,\cdot)\) \(\chi_{3751}(607,\cdot)\) \(\chi_{3751}(634,\cdot)\) \(\chi_{3751}(722,\cdot)\) \(\chi_{3751}(732,\cdot)\) \(\chi_{3751}(754,\cdot)\) \(\chi_{3751}(772,\cdot)\) \(\chi_{3751}(888,\cdot)\) \(\chi_{3751}(948,\cdot)\) \(\chi_{3751}(975,\cdot)\) \(\chi_{3751}(1063,\cdot)\) \(\chi_{3751}(1073,\cdot)\) \(\chi_{3751}(1095,\cdot)\) \(\chi_{3751}(1113,\cdot)\) \(\chi_{3751}(1185,\cdot)\) \(\chi_{3751}(1229,\cdot)\) \(\chi_{3751}(1289,\cdot)\) \(\chi_{3751}(1316,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{39}{110}\right),e\left(\frac{2}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(50, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{73}{165}\right)\) |