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.ed
\(\chi_{3751}(26,\cdot)\) \(\chi_{3751}(37,\cdot)\) \(\chi_{3751}(119,\cdot)\) \(\chi_{3751}(181,\cdot)\) \(\chi_{3751}(192,\cdot)\) \(\chi_{3751}(212,\cdot)\) \(\chi_{3751}(223,\cdot)\) \(\chi_{3751}(367,\cdot)\) \(\chi_{3751}(378,\cdot)\) \(\chi_{3751}(460,\cdot)\) \(\chi_{3751}(471,\cdot)\) \(\chi_{3751}(522,\cdot)\) \(\chi_{3751}(533,\cdot)\) \(\chi_{3751}(553,\cdot)\) \(\chi_{3751}(564,\cdot)\) \(\chi_{3751}(708,\cdot)\) \(\chi_{3751}(719,\cdot)\) \(\chi_{3751}(801,\cdot)\) \(\chi_{3751}(812,\cdot)\) \(\chi_{3751}(863,\cdot)\) \(\chi_{3751}(894,\cdot)\) \(\chi_{3751}(905,\cdot)\) \(\chi_{3751}(1060,\cdot)\) \(\chi_{3751}(1142,\cdot)\) \(\chi_{3751}(1153,\cdot)\) \(\chi_{3751}(1204,\cdot)\) \(\chi_{3751}(1215,\cdot)\) \(\chi_{3751}(1235,\cdot)\) \(\chi_{3751}(1246,\cdot)\) \(\chi_{3751}(1390,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{51}{55}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{41}{66}\right)\) |