Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3971.bk
\(\chi_{3971}(18,\cdot)\) \(\chi_{3971}(94,\cdot)\) \(\chi_{3971}(151,\cdot)\) \(\chi_{3971}(189,\cdot)\) \(\chi_{3971}(227,\cdot)\) \(\chi_{3971}(303,\cdot)\) \(\chi_{3971}(398,\cdot)\) \(\chi_{3971}(436,\cdot)\) \(\chi_{3971}(512,\cdot)\) \(\chi_{3971}(569,\cdot)\) \(\chi_{3971}(607,\cdot)\) \(\chi_{3971}(645,\cdot)\) \(\chi_{3971}(778,\cdot)\) \(\chi_{3971}(816,\cdot)\) \(\chi_{3971}(854,\cdot)\) \(\chi_{3971}(930,\cdot)\) \(\chi_{3971}(987,\cdot)\) \(\chi_{3971}(1025,\cdot)\) \(\chi_{3971}(1063,\cdot)\) \(\chi_{3971}(1139,\cdot)\) \(\chi_{3971}(1196,\cdot)\) \(\chi_{3971}(1234,\cdot)\) \(\chi_{3971}(1272,\cdot)\) \(\chi_{3971}(1348,\cdot)\) \(\chi_{3971}(1405,\cdot)\) \(\chi_{3971}(1481,\cdot)\) \(\chi_{3971}(1557,\cdot)\) \(\chi_{3971}(1614,\cdot)\) \(\chi_{3971}(1652,\cdot)\) \(\chi_{3971}(1690,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{11}{190}\right)\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{73}{190}\right)\) | \(e\left(\frac{9}{190}\right)\) | \(e\left(\frac{93}{95}\right)\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{27}{38}\right)\) |