Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 3997.cf
\(\chi_{3997}(82,\cdot)\) \(\chi_{3997}(124,\cdot)\) \(\chi_{3997}(143,\cdot)\) \(\chi_{3997}(236,\cdot)\) \(\chi_{3997}(285,\cdot)\) \(\chi_{3997}(339,\cdot)\) \(\chi_{3997}(376,\cdot)\) \(\chi_{3997}(418,\cdot)\) \(\chi_{3997}(899,\cdot)\) \(\chi_{3997}(1067,\cdot)\) \(\chi_{3997}(1146,\cdot)\) \(\chi_{3997}(1158,\cdot)\) \(\chi_{3997}(1398,\cdot)\) \(\chi_{3997}(1412,\cdot)\) \(\chi_{3997}(1515,\cdot)\) \(\chi_{3997}(1538,\cdot)\) \(\chi_{3997}(1578,\cdot)\) \(\chi_{3997}(1585,\cdot)\) \(\chi_{3997}(1711,\cdot)\) \(\chi_{3997}(2075,\cdot)\) \(\chi_{3997}(2096,\cdot)\) \(\chi_{3997}(2166,\cdot)\) \(\chi_{3997}(2222,\cdot)\) \(\chi_{3997}(2243,\cdot)\) \(\chi_{3997}(2252,\cdot)\) \(\chi_{3997}(2313,\cdot)\) \(\chi_{3997}(2434,\cdot)\) \(\chi_{3997}(2504,\cdot)\) \(\chi_{3997}(2593,\cdot)\) \(\chi_{3997}(2726,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{34}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(82, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{107}{114}\right)\) |