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.di
\(\chi_{3751}(35,\cdot)\) \(\chi_{3751}(39,\cdot)\) \(\chi_{3751}(250,\cdot)\) \(\chi_{3751}(326,\cdot)\) \(\chi_{3751}(376,\cdot)\) \(\chi_{3751}(380,\cdot)\) \(\chi_{3751}(591,\cdot)\) \(\chi_{3751}(667,\cdot)\) \(\chi_{3751}(721,\cdot)\) \(\chi_{3751}(932,\cdot)\) \(\chi_{3751}(1058,\cdot)\) \(\chi_{3751}(1273,\cdot)\) \(\chi_{3751}(1349,\cdot)\) \(\chi_{3751}(1399,\cdot)\) \(\chi_{3751}(1403,\cdot)\) \(\chi_{3751}(1614,\cdot)\) \(\chi_{3751}(1690,\cdot)\) \(\chi_{3751}(1740,\cdot)\) \(\chi_{3751}(1744,\cdot)\) \(\chi_{3751}(1955,\cdot)\) \(\chi_{3751}(2031,\cdot)\) \(\chi_{3751}(2081,\cdot)\) \(\chi_{3751}(2085,\cdot)\) \(\chi_{3751}(2372,\cdot)\) \(\chi_{3751}(2422,\cdot)\) \(\chi_{3751}(2426,\cdot)\) \(\chi_{3751}(2637,\cdot)\) \(\chi_{3751}(2713,\cdot)\) \(\chi_{3751}(2763,\cdot)\) \(\chi_{3751}(2767,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{81}{110}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) |