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.dc
\(\chi_{3751}(194,\cdot)\) \(\chi_{3751}(281,\cdot)\) \(\chi_{3751}(283,\cdot)\) \(\chi_{3751}(535,\cdot)\) \(\chi_{3751}(574,\cdot)\) \(\chi_{3751}(622,\cdot)\) \(\chi_{3751}(624,\cdot)\) \(\chi_{3751}(876,\cdot)\) \(\chi_{3751}(915,\cdot)\) \(\chi_{3751}(963,\cdot)\) \(\chi_{3751}(1217,\cdot)\) \(\chi_{3751}(1256,\cdot)\) \(\chi_{3751}(1306,\cdot)\) \(\chi_{3751}(1558,\cdot)\) \(\chi_{3751}(1597,\cdot)\) \(\chi_{3751}(1645,\cdot)\) \(\chi_{3751}(1647,\cdot)\) \(\chi_{3751}(1899,\cdot)\) \(\chi_{3751}(1938,\cdot)\) \(\chi_{3751}(1986,\cdot)\) \(\chi_{3751}(1988,\cdot)\) \(\chi_{3751}(2240,\cdot)\) \(\chi_{3751}(2279,\cdot)\) \(\chi_{3751}(2327,\cdot)\) \(\chi_{3751}(2329,\cdot)\) \(\chi_{3751}(2620,\cdot)\) \(\chi_{3751}(2668,\cdot)\) \(\chi_{3751}(2670,\cdot)\) \(\chi_{3751}(2922,\cdot)\) \(\chi_{3751}(2961,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{37}{110}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(194, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(1\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(1\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) |