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.dh
\(\chi_{3751}(201,\cdot)\) \(\chi_{3751}(240,\cdot)\) \(\chi_{3751}(246,\cdot)\) \(\chi_{3751}(368,\cdot)\) \(\chi_{3751}(542,\cdot)\) \(\chi_{3751}(581,\cdot)\) \(\chi_{3751}(587,\cdot)\) \(\chi_{3751}(709,\cdot)\) \(\chi_{3751}(883,\cdot)\) \(\chi_{3751}(922,\cdot)\) \(\chi_{3751}(1050,\cdot)\) \(\chi_{3751}(1224,\cdot)\) \(\chi_{3751}(1263,\cdot)\) \(\chi_{3751}(1269,\cdot)\) \(\chi_{3751}(1391,\cdot)\) \(\chi_{3751}(1565,\cdot)\) \(\chi_{3751}(1604,\cdot)\) \(\chi_{3751}(1610,\cdot)\) \(\chi_{3751}(1732,\cdot)\) \(\chi_{3751}(1906,\cdot)\) \(\chi_{3751}(1951,\cdot)\) \(\chi_{3751}(2073,\cdot)\) \(\chi_{3751}(2247,\cdot)\) \(\chi_{3751}(2286,\cdot)\) \(\chi_{3751}(2292,\cdot)\) \(\chi_{3751}(2414,\cdot)\) \(\chi_{3751}(2588,\cdot)\) \(\chi_{3751}(2627,\cdot)\) \(\chi_{3751}(2633,\cdot)\) \(\chi_{3751}(2755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{39}{55}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(201, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) |