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.cs
\(\chi_{3751}(15,\cdot)\) \(\chi_{3751}(91,\cdot)\) \(\chi_{3751}(302,\cdot)\) \(\chi_{3751}(306,\cdot)\) \(\chi_{3751}(356,\cdot)\) \(\chi_{3751}(432,\cdot)\) \(\chi_{3751}(643,\cdot)\) \(\chi_{3751}(647,\cdot)\) \(\chi_{3751}(697,\cdot)\) \(\chi_{3751}(773,\cdot)\) \(\chi_{3751}(984,\cdot)\) \(\chi_{3751}(988,\cdot)\) \(\chi_{3751}(1038,\cdot)\) \(\chi_{3751}(1114,\cdot)\) \(\chi_{3751}(1325,\cdot)\) \(\chi_{3751}(1329,\cdot)\) \(\chi_{3751}(1379,\cdot)\) \(\chi_{3751}(1666,\cdot)\) \(\chi_{3751}(1670,\cdot)\) \(\chi_{3751}(1720,\cdot)\) \(\chi_{3751}(1796,\cdot)\) \(\chi_{3751}(2007,\cdot)\) \(\chi_{3751}(2011,\cdot)\) \(\chi_{3751}(2061,\cdot)\) \(\chi_{3751}(2137,\cdot)\) \(\chi_{3751}(2348,\cdot)\) \(\chi_{3751}(2352,\cdot)\) \(\chi_{3751}(2402,\cdot)\) \(\chi_{3751}(2478,\cdot)\) \(\chi_{3751}(2693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{26}{55}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) |