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.ef
\(\chi_{3751}(48,\cdot)\) \(\chi_{3751}(75,\cdot)\) \(\chi_{3751}(135,\cdot)\) \(\chi_{3751}(179,\cdot)\) \(\chi_{3751}(291,\cdot)\) \(\chi_{3751}(301,\cdot)\) \(\chi_{3751}(389,\cdot)\) \(\chi_{3751}(416,\cdot)\) \(\chi_{3751}(476,\cdot)\) \(\chi_{3751}(520,\cdot)\) \(\chi_{3751}(592,\cdot)\) \(\chi_{3751}(610,\cdot)\) \(\chi_{3751}(642,\cdot)\) \(\chi_{3751}(730,\cdot)\) \(\chi_{3751}(757,\cdot)\) \(\chi_{3751}(817,\cdot)\) \(\chi_{3751}(861,\cdot)\) \(\chi_{3751}(933,\cdot)\) \(\chi_{3751}(951,\cdot)\) \(\chi_{3751}(973,\cdot)\) \(\chi_{3751}(983,\cdot)\) \(\chi_{3751}(1071,\cdot)\) \(\chi_{3751}(1158,\cdot)\) \(\chi_{3751}(1202,\cdot)\) \(\chi_{3751}(1274,\cdot)\) \(\chi_{3751}(1292,\cdot)\) \(\chi_{3751}(1314,\cdot)\) \(\chi_{3751}(1324,\cdot)\) \(\chi_{3751}(1439,\cdot)\) \(\chi_{3751}(1499,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{46}{55}\right),e\left(\frac{7}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(48, a) \) | \(-1\) | \(1\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{233}{330}\right)\) |